The accelerating universe is the observation that the universe appears to be expanding at an increasing rate. In 1998 observations of Type Ia supernovae suggested that the expansion of the universe is accelerating^[1][2] since around redshift of z~0.5^[3].

The Supernova Cosmology Project is one of two research teams that determined the likelihood of an accelerating universe and therefore a positive Cosmological constant. This discovery was named "Breakthrough of the Year for 1998" by Science Magazine^[1] and, along with the High-z Supernova Search Team, the project team won the Gruber Prize in Cosmology in 2007.^[2]

The project uses data from the redshift of Type Ia supernovae.

The project is mainly based at Lawrence Berkeley National Laboratory. The international team with 31 members from Australia, Chile, France, Spain, Sweden, UK and USA is headed by Saul Perlmutter

The High-z Supernova Search Team was an international cosmology collaboration which used Type Ia Supernovae to chart the expansion of the Universe. The team was formed in 1994 by Brian P. Schmidt, then a post-doctoral research associate at Harvard University, and Nicholas B. Suntzeff, a staff astronomer at the Cerro Tololo Inter-American Observatory in Chile. The team expanded to roughly 20 astronomers located in the United States, Europe, Australia, and Chile. They used the Victor M. Blanco Telescope of CTIO to discover Type Ia supernovae out to redshifts of z=0.9. The discoveries were verified with spectra taken mostly from the telescopes of the Keck Observatory, and the European Southern Observatory.

In a 1998 study led by Adam Riess, the High-z Team became the first to publish evidence that the expansion of the Universe is accelerating (Riess et al. 1998, AJ, 116, 1009, submitted March 13, 1998, accepted May 1998). The team was managed by Brian P. Schmidt of the Mount Stromlo Observatory, which is part of the Australian National University. The team later spawned Project ESSENCE led by Christopher Stubbs of Harvard University and the Higher-z Team led by Adam Riess of Johns Hopkins University and Space Telescope Science Institute.

In the past few years, these observations have been corroborated by several independent sources: the cosmic microwave backgroundand large scale structure^[4], age of the universe^[5] , as well as improved measurements of the supernova, ^[6][7] and X-ray properties of galaxy clusters.

Density drops
An expanding universe means that density drops due to continual space being added between all matter. If acceleration continues, eventually all galaxies beyond our own Local supercluster will redshift so far that it will become hard to detect them, and the distant universe will turn dark.

Explanatory models

Models attempting to explain accelerating expansion include some form of dark energy: cosmological constant, quintessence, or phantom energy, with the latest WMAP data favouring the cosmological constant. The most important property of dark energy is that it has negative pressure which is distributed relatively homogeneously in space.

Divergent expansion

Phantom energy in a scenario known as the Big Rip causes an exponentially increasing divergent expansion, which overcomes the gravitation of the local group and tears apart our Virgo supercluster, it then tears apart the milky way galaxy, our solar system, and finally even atoms. Measurements of acceleration are thought crucial to determining the ultimate fate of the universe, however we should expect the implications of such a major discovery to develop slowly over many years in the same way the big bang model has continued to develop.

Dark energy dominates

As the Universe expands, the density of dark matter declines more quickly than the density of dark energy (see equation of state) and, eventually, the dark energy dominates. Specifically, when the volume of the universe doubles, the density of dark matter is halved but the density of dark energy is nearly unchanged (it is exactly constant for a cosmological constant).

Foreword by John Shadow:

The above references will lead the interested reader into a bewildering kaleidoscope of models and ideas, attempting to 'make sense' of the scientific measurements of the supernovae data collected by the stated research teams.

The final conclusion found in the references and the websearches are however all based on fundamentally flawed physical assumptions.
Whilst the measurements are all validated; the text book and standard expositions of the modern cosmology community are not.
Ultimately all of these valid measurements measured just one thing, namely the light emitted from some object in the universe, separated from the receiver apparatus by a finite distance and a finite time interval to get to the receiver from the emitter and its clocks and rulers measuring time and space respectively.

There are a number of cosmologists, who have realised those "flawed assumptions" and have proposed alternative hypothesises, mainly engaging higher dimensional spacetimes in connection with bubble-universes; ekpyrotic brane collisions and other multiverse scenarios.

What are these  "flawed" assumptions? The underpinning "flaw" is the concept of a comoving reference frame (April's expanding room and ruler) creating the space it occupies. Iow, there is no space between the far away mirror and April's room or more fundamentally, this far away mirror does not exist.

April defines the fixed ruler in the constancy of lightspeed c=lightpath X/time t and sets the distance from herself to the far away mirror as lightpath X=R_max=R_Hubble=R_H=ct_{AgeofUniverse}.
As this distance becomes "fixed" in the lightpath and the constancy of the speed of light; the Age of the Light-Invariant or Electromagnetic Universe also becomes fixed in the time it would take light to travel from the Mirror of Eternity to the Mirror of the Limits.

1. April's Growing Room and her Gravity

April then realises something.
'Hold on, my room is expanding as a kind of subuniverse or nested or fractal selfsimilar universe.
So if my room would travel and expand at lightspeed, then it would take a finite time interval, namely the Age of the Universe, to reach the far away mirror.
But what then? Will my room then bounce back and skrink again or will my room shatter this far away mirror and continue expanding at this lightspeed'?

But then April has an eureka moment. She realises that her expansion is slowing down and so her room, in getting more and more the size of the "greater universe" in the approach of the mirrors, could very well never reach this far away mirror yet approaching it ever more closely in an asymptotic approach.
April, knowing a little mathematics, envisages an expanding series of the form: 0/1+1/2+2/3+3/4+...+n/(n+1)+...99999/1000000+...always getting bigger as a fraction or a decimal but never actually reaching the limit of 1/1=1.
This was April's own beginning as the Mirror of the Infinity in 0/0=∞/∞=1, because 0=0 and ∞=∞ to define the inversion of 1/1=1 in the undefinability of  1/0≡∞ ↔ ∞.0≡1  and limited in the mathematical symbolisation in the physicalisations of limits in  1/∞→0  and  1/0→∞ as the reciprocities of each other by  0/1≡0  and  ∞/1≡∞.
 
April then allows for both possibilities of the lightpath in accomodating two kinds of expansion and as reflected in her observation of the two rulers appropriate for the measurement of distances - the expanding comoving metric of the ruler in her room and the static ruler as defined by the speed of light.
April imagines the lightspeed to not only outrun the asymptotic approach, but also for this lightpath to become reflected back into the path of her expanding room, as well as "breaking through" the far away mirror in a refractive manner of continuation.

'But hold on, there would then have to be a fundamental difference between the reflected lightpath and the refracted lightpath due to the intersection of the returning lightpath with the path of my room's expansionary journey.
Why is my room's expansion slowing down in deceleration relative to the constancy of the lightpath', April thought?

'It must be because of me. If I wouldn't be here, then this room would be as big as the "outer space" and the spherical mirror would be identical to the far away mirror and this slow-down would not be necessary.
What is it about me, that slows the speed of this room down'?
April decides to call this tendency her inertia, related to some measurement of her weight and her mass and she terms the "outside space" the gravity acting on her room concentrated in her mass.
Then April remembered something more about her previous existence in the mirror wonderland of the Mirror of Infinity.
This thing called gravity was actually a "force of attraction" between the mirrors.
There was this self-gravity confined to April's room which was attracted to the self-gravity of the far away mirror.
'If now I could express this self-gravity of my room as being information mapped onto the far away mirror and vice versa having the self-gravity of the far away mirror mapped as information onto this spherical mirror; then in this gravitational interaction, I could find out what this asymptotic approach is in terms of universal gravitation.
Perhaps the self-gravity could then be used in a form of a dimensional intersection of the lightpath and in a gravitational physics of self- and mutual interaction of Black Holes as two-dimensional surfaces or manifolds in view of the surface properties of the approaching- and receding mirrors and the information transfers between them'.

2. April throws her weight around, builds a house and finds her Cat called Brooke

April decided to label her own weight as Big-M-Zero or M_o to allow her to use shortcuts in the description of her discoveries about the cosmos at a later stage and when so appropriate.
'Ok', April thought; 'as I am to only thing here in this empty spherical room; I might as well say that my M_o is the weight of this little universe, which has nothing else within it'.
April looked into her reflection before her eyes and became irritated. 'I am the goddess of this local universe and I am all alone in here. Here I am like a little baby, being born naked from the womb. Look at my hair; it is such a mess!'
Then, as April shook her head, she saw a single hair falling towards the floor of the spherical mirror.
April caught the strand of hair and decided to place it some distance away from her, someplace in her room.
'This strand of hair is a part of me and I might as well begin to talk and think to myself, she uttered'.
Just as April retreated something strange happened to the strand of hair. It began to glow in some self-irradiant essence and then became transparent and disappeared to reappear as a pair of scissors.
'What a magnificent magical transformation', April thought. 'This part of me became another part of me, but rather more useful'.
April resculpted her hair in the style of an Egyptian queen from the Nile and an imaginary scenario which seemed to flash from nowhere into her mind.
April cut a number of strands of hair and then distributed the strands all around her room.
'Perhaps the magic in this room will give some more useful tools and surprises', so she thought.

The magic started with walls, stairways, doors and windows and some strands of hair turned into furniture, ornaments, utilities and computers.

'Wow, all this is part of me and seems to be a redistribution and transformation of part of my total weight M_o.
I shall honour this room of mine, where I did begin my magic tricks as my "Special Room", my sanctuary, where I shall treasure the little circular window through which I can see the far away mirror. This shall become my "Special Place" where I shall try to figure out what is going on in this spherical universe of mine; both qualitatively in the telling of  "My Story" and quantitatively in a formal language of science and of mathematics'.

April explored, arranged and defined "her room", which had become "her house" in her "throwing her weight around".
'I'll have to figure this gravity thing out', April pondered; 'but now I know that whatever I am gravitationally, can be partitioned and made into many smaller and interrelated parts'.

April cut another single strand of her hair and looked at it.
'If you just could talk to me; I now have discovered the magic of the universe, but have noone to talk to'.
With these words, the strand of hair became luminous, transparent and then metamorphosed into a ginger cat.
'Meow Omm meow', said Brooke, the cat as she looked at April.
'Part of me has become a cat', April shouted exuberantly; 'now I have another living thing in my universe and now I can gravitationally interact with myself to solve the mysteries'!

'It's better than that April', said Brooke - 'I am a talking cat from wonderland'.

'And I am a goddess too', continued Brooke; 'just like you and just like you I have entered the Mirrorland of the Limits from the outside of the Mirrorland of the Infinity.
I am your cat in this room and simultaneously you are my cat in my room. Yet there is only the one room or should I say this house, which is a town and a city and a continent and a planet and a solar system and a galaxy and a galaxy group and a supercluster all nested in selfsimilarity in the universe, limited however in the little circular window.

There are strands in your hair, which are many many things April. I have learned this from some of my broken fingernails; some turned into things and others changed into crystals, plants, animals and intelligences of all sorts.
Some of those sentiences know about philosophy and science and what the expanding room signifies in the greater order of things.
I have learned some things, but not everything. There is much to explore and to discover and as four eyes see more than two; the selfrelativity between us has engaged this communication.
I have become one brick in your house and you have become one brick in my individuated house'.

'How wonderful', said April. 'I understand you are like a biological somatic cell or a neuron in my body and so am I in yours'.

'Indeed', replied Brooke 'and allow me to inform you about this gravity thing, as far as I myself understand it from the information given by the natural philosophers.
You Big-M-Zero April is the key. As you have seen, you can easily take part of you and transform its energy into other forms. It doesn't matter if you term this the magic of evolution or the magic of technological inventiveness.
The strand of hair of you, which you experience as your cat Brooke is mapped or mirrored in a strand of my hair with the result, that I have a cat called April in my selfrelative universe.

You know the little circular loop in our special rooms; the one which shows us the far away mirror?
Your M_o being here is mapped as my M_o being there and vice versa. We are total reflections of each other on the grandest scale possible; namely the scale between the Inside Mirror here and the Outside Mirror far away.
So only in the partiality of ourselves are we each other's cat. I have found out, that this partiality of distributing our weight around in this spherical universe defines two sorts of gravity.
The one here in our houses is a local gravity, which acts differently to the overall gravity where the weights are not distributed in the planets, stars, galaxies, superclusters and so on.
So in here the laws of physics become locally applied as in the formulations of General Relativity, where the matter curves space and space interacts with the matter in a dynamical way of those things termed the metrics.
But "out there", the spacetime curvature acts nonlocally in treating the mirrors as the only occupants of the "collectrively and holistically integrated" extra-dimensional spacetime.   
Our M_o's are so mapped as overall gravities and obey mathematical and physical lwas of nature, which are much simpler than the laws of gravity of the local universe. This is because the local gravity is of a lower dimension, than the encompassing gravity.

You and I are explicitely defined in being made up of minimum masses. These minimum masses m_min are however not the same in the two dimensions , say the spherical inside and the extraspherical or toroidal outside, namely the spacetime from outside the loopey window to the far away mirror.

Ok, April, I'll try to recall something one of the natural philosphers has said and written.

N.m_minc²=G_oM_o²/R_min
is the formula for the Gravitational Potential Energy between our two M_o's and where N counts how many of those 'smallest possible' weight bits are in the 'higher dimension' of the 'higher dimensional' gravity. I recall the cosmologist saying, that the R_min is a particular location within this room and which is symmetrically coupled to the M_infinity=M_∞ , which is the Big M-Infinity allowing the far away mirror to become gravitational from the higher dimension.
So it is like this in the greater picture. The M_o is a form of energy, which can be expressed in the gravitational potential energy (GPE) as a gravitational self-interaction. This is the idea that things can collapse 'under their own weight'.
Then the GPE expressed in Einstein's mass-energy equation E=mc² becomes reformulated as 'holes in spacetime' and are called 'Black Holes' with a characteristic size R_{Schwarzschild}=R_S=2G_oM/c². This describes a 'curvature of spacetime' and related as to why this house seems to be a spherical enclosure.

The GPE between the M_o's, namely you and I is so different from the GPE between the M_∞ and the M_min, the latter being the particular Big-M, which is smaller than our totality M_o's, and so can be the coupling Big-M to the Big-M-Infinity'.

'Yes, I see the difference', April replied. 'Both of our M_o's are within the smaller spherical universe and being the same, can be mapped onto the far away mirror respectively. But the M_infinity must be coupled to something in this smaller spherical universe, as the Big-M-Infinity is not in the smaller universe. And because the M_o's are taken, the particular Big-M must be smaller than our totals and also therefore this partitioning of M_o becomes possible'.

'Yes, April and now the GPE looks just a little different and relates to something the scientists call the Zero-Point-Energy or ZPE.
You see the m_min's are not mass at all, but become so in the redistribution of the total mass of the spherical universe in our houses.
The m_min's are actually massless superstrings and so both you and I are physically speaking just a collection of superstrings or supermembranes.
The smallest possible supermembrane has this minimum mass equivalent, which can become inertial from a previous noninertial state, namely that of a massless bosonic supermembrane.

This is defined by the physicists as a minimum ZPE-Oscillator:
E_min=½hf_min=½kT_min=½m_minc².

So now the GPE for the mass partition inside the smaller universe of our houses couples to the Infinity-Mass like:

N.½m_minc²=G_oM_∞M_min/R_min

Putting the GPE's for the gravitational self-coupling and the mutual dimensional coupling together,
then shows that 2M_∞M_min=M_o².
What this M_min is and how it helps to solve the gravitational mysteries I don't know as yet. Perhaps we can work on this together. This is one of the reasons I decided to become your talking cat, to allow our two houses as the one M_o to interact across the dimensions'.
'It seems, that gravity is a leaking interaction from those higher dimensions', April replied.


3. April's 'Arachne de Gaea' and her Eagle 'Mac the Knife'

One day, April was in her "special room", which she had named Arachne de Gaea or the "Spider of Gaia". Brooke had run off into another room in April's house to do her own thing; conversing with some of the old philosphers, she had met and for the purpose to find out more about the purposes of the duality between the wonderland and the mirrorland.

April had manifested many more "creatures" as part of herself, including Billy the Terrier, who loved to catch and chase little white balls in one of April's rooms, which had manifested as a big park.
Then one day in her "special room" some part of April magically transformed into a big hairy spider, who then wove a big web in a corner of the "special room" and as it expanded so did this intricately woven spider's web.
April then knew that this was a symbol for her sanctuary, a protector of sorts as Grandma Spider-Woman.
April did not know what her house needed protection from; but she thought it possible that some parts of herself, being alive as themselves, could possibly forget where they had come from, namely from April and could then begin not to like her any more in their forgetfulness.
So Arachne de Gaea was April's own remembrance not to forget, that the parts of herself, which might begin to attack her in some fashion, were truly parts of herself, which had forgotten their origins.

So one day, April peered through the loopey window to see herself in the far away mirror.
'I wonder if Arachne de Gaea is also a remembrance for myself as the goddess', April thought.
'It must be', April realised. 'I entered mirrorland from the opposite direction and the image of the far away mirror is here within this my own sanctuary.
If Brooke is right and the expansion of this place of the spider can never reach the far away mirror because of its asymptotic deceleration, then it would be ultimately futile to engage in whatever journey within mirrorland to reenter wonderland.

As manifested goddess in 3-dimensional mirrorland I can then never hope to rediscover myself as a 4-dimensional goddess in wonderland again'.

'But you can go backwards and where you entered right in this room', said Grandma Spiderwoman.

'Wow', exclaimed April; 'this is the first time this spider talked; but if Brooke the Cat can talk, maybe all living things in my house are enabled to talk in some way.
Yes, Grandma is right', thought April; 'I can never get to my final destination of the far away mirror of this, my expanding house, in going forwards; but in retracing my steps backwards I don't have to go far at all'.

So April walked backwards towards the image of the far away mirror on the wall in her special room - and got stuck.
Try as she might, she could not pass through the wall of the spherical mirror from which she had entered mirrorland from wonderland.

'I am well and truly trapped in my house', April thought. 'Why was it so easy to be born into this place and yet it seems impossible to leave this place'.

'You are required to realise your image in the far away mirror my dear', Grandma Spiderwoman spoke again.
'You are stuck in the 3rd space-dimension for the reason to manifest the boundlessness of wonderland in the limitations of mirrorland.
Though you cannot reach the far away mirror in using the tools of the 3rd dimension, you can do so using the tools of the 4th dimension of space.
Turn around and look into the image of the image of yourself. The goddess April in the inaccessible far away mirror is reflected in the goddess April you can touch on the mirror on the wall.
"Who is the prettiest goddess of them all" - you are, because all goddesses are you as the image in the far away place and yet individuated in the special rooms in the one house'.

'Ah', said April, 'I got it. I am in my special room and Brooke and Billy are in their special rooms; and all of us are looking at our individiuated images within those rooms, but become the "prettiest and most splendid unified image" in the far away mirror.
Then I am stuck in mirrorland, because I am an individuated goddess'.

'You got it my darling daughter', said Grandma Spiderwoman.
'Allow me to introduce to yourself yet another part of you. It is a natural philosopher like the ones Brooke has mentioned to you. Have a look at your right side April'.

April looked to her right and saw a majestic looking eagle appear, sitting on a branch of an old oaken tree, which had materialised simultaneously with the eagle.

April saw sharp talons on the eagle, with whom he clawed the oaken branch.
'How are you eagle', April said. 'You are some fearsome creature of mine and I shall call you Mac the Knife due to your ferocious looking demeanour'.

'Hello my dear', said Mac the Knife; 'yes I have come to share with you some of the wisdom of the natural philosophers. I am an old warrior April. I have been around this house for a long time; even before you entered mirrorland and even before you did discover the magic in this place.

But as soon as Grandma Spiderwoman had woven her web of the protegees; I was enabled to manifest to help you and your familiars on your journeys towards wonderland.
Some of the things I shall share with you might be a little hard to understand at first, but with help of all of your friends, the stories should get clearer and clearer in time.

Being one of the 'Old Wisdom keepers'; I shall give you information in a more technical manner; such as the equations which your cat Brooke has remembered from her philosophy courses.

So this room of yours is a mirrorland room and this room expands towards the far away mirror.
If you now try to measure distances in this room, your rulers will expand in the same way as the room to remain consistent. A displacement of 10 metersticks can only remain 10 metersticks, if the meterstick changes into a 2 meterstick, when the room as expanded to double its size of the time of the 1 meterstick. So using the 1 meterstick as a "metric" will cause you trouble to accurately measure the distance to the far away mirror.

In technical language of the natural philosophers using a 3D perspective then;  the metric expansion is thought to "stretch" the metric, causing all sorts of difficulties to determine the distances to cosmological objects in the varying distance scales and its relationship to the postulates of Special Relativity and its lightspeed invariance as the constancy of the speed of light.

For an example: If in 1 billion years the metric stretches to double the size it was when say a star emitted a lighpulse; then the time of the emission of the light 1 billion years later would not infer a distance of 1 billion lightyears but a distance of 2 billion lightyears relative to the observer, measuring the lightpulse after 1 billion years.

This scenario would disallow utility of the Special Relativity formalism, especially the Relativistic Doppler Effect, because the stretching of space could exceed lightspeed.

In your  case however; the application of Special Relativity is both sufficient and appropriate, as long as the "light emitters" are measured in the fixed metric of the far away mirror space.

Applying Occam's Razor of the parsimony, crystallizes a preferred cosmological model immediately.

A major understanding for you so is the realisation that you should use a "fixed" meterstick of the lightspeed invariance in measuring the distance between the two mirrors as a reference standard; the one you entered from and the far away one. But you see, you cannot measure anything, because you do not know how distant the far away mirror is'.

'So what do I do', asked April and wondering if Mac the Knife knew the answer to his own disposition'?

'Hehe', Mac the Knife giggled to himself. He knew what April was thinking, being an enlightened part of her; 'I do know the answer my dear. The answer is found in knowing how the far away mirror got there in the first place.

Whilst the universe expands, this expansion in 4-dimensional Euclidean-Minkowski-spacetime does not require to be an expansion into some hitherto undefined realm, then becoming defined as a metric spacetime by that. The assumption here is the physical universe to be a selfcontained entity without any boundary separating the selfcontained universe as observed from within from the necessity of such observation from a without.
The beginning of this expansion is colloquially termed the Quantum Big Bang, followed by an Inflationary Epoch, lasting a minute fraction of a second of about 10^-32 seconds and smaller than a defined Planck-Time:  t_P=h/2πm_Pc²=√(hG_o/2πc⁵)~6x10^-44 seconds by a factor of about a trillion.

The quantum universe is a selfcontained entity without boundary as measurable from within, but the emergence of this entity from its boundless selfstate manifested the entity as a particular boundary as measurable from without by a postulated mirror symmetry.

The Quantum Big Bang did not occur at the Planck-Time, but at the Inflaton-Time t_inflaton=f_min.
Then the Inflationary Epoch of the standard model preceded the Quantum Big Bang, instead of following it.
If this presumption is valid, then the inflaton manifests a boundary for the universe from within and as observed from the without.
The without observer is located at the boundless coordinate of the 'NullTime, which is 0 as a "Singularity" and not physically finitizable like the Planck-Time.
The "Singularity" manifests the Planck-Time as the observer from within however and so the metricication of the universal entity becomes defined in physicality initially.

The Null-Time observer can then be defined as a Mirror without the physicality.
This is like the simple analogy of someone trying to enter mirrorland as an Alice in Wonderland.
Iow the boundless observer without the physical universe is Alice who has entered the mirror and is then in mirrorland and becomes renamed as April.
But Alice could then step back into wonderland with April remaining in mirrorland as Alice's Shadow to become a doubled observer within and without the physical universe and in doing so, Alice would be able to look at the mirror she has just come out from on the other side of the universe and which might be just the size of a room at that stage.

The boundary of the universe is a spherical mirror and defines the inside observer aka Inside-April as being also Outside-Alice depending on her choosing to experience the spacetime of the physical universe within as April or the boundlessness outside as Alice.

It is the inflation, which created the inside spacetime of the doublesided mirror.
The minimum spacetime can be associated with the Planck-Spacetime and the maximum with some multiple of this Planck-spacetime.
It is this maximum, which is referenced as the Hubble-Radius R_Hubble=R_H of the observable universe and it is this minimum which is generally assumed to be the Planck-Radius R_Planck=L_P=√(hG_o/2πc³).
The inflation then manifests the maximum from the minimum in selfsimilarity and the labellings of a holofractal and holographic universe reflected in the quantisation of the minimum spacetime configuration of the Planck-Scale or its string-membrane magnification, say in different string classes obeying particular symmetries.

A particular modification of Membrane-Theory has established the inflation parameters as follows:

De Broglie matterwave speed:  R_Hubble.f_inflaton=R_H.f_i =R_Hc/λ_inflaton~4.793..x10⁵⁶ m/s
De Broglie matterwave acceleration:   R_Hubble.f_inflaton²=R_H.f_i² ~1.438x10⁸⁷ m/s²

The inflation parameters relate to the Planck parameters in the c-invariance c=f_iλ_i=2πL_Pf_P 
The inflaton parameters are precisely linked to the gravitational string parameters in coupling to the quantization of mass as indicated in your discourse with your cat Brooke.
But I shall leave a more detailed exposition just what this is for another time'.

'Thank you Mac', said April. 'These descriptions of yours require some processing. I have understood only your outline, but my recording device here has copied your description in the form of alphanumerical symbolisms and my friends and I shall add your information to our collective data base for further and continuing examination.
But having friends like you, shall surely allow us all to figure out this thing called gravity and the distribution of my weight as the Big-M-Zero'.

'Yes April; you will find that the gravity relating the wonderland to the mirrorland is the Quantum Gravity connecting the large macro universe of the General Relativity to the micro universe of the Special Relativity', answered Mac the Knife.

4. April visits her Galaxy with Cindy her Dolphin from the Stars

One day after awakening from a peaceful slumber, April wished to ask Grandma Spiderwoman a question about Grandpa.
As April went to the corner of her room, where Grandma had woven her web, the web was there, but Grandma was not.

'Where are you Grandma Spiderwoman', April shouted?

'Turn around, I am right behind you in the far left corner of your room', Grandma replied.

As April turned about, she saw another big and magnificently woven web-tapestry taking form in the corner of her room adjacent to the older web already spun.

'What are you doing Grandma', asked April?

'I am preparing your room for its transformation April', Grandma replied.
'You already know that everything in this room is part of you and including myself as your Grandma. But as you are creating more and more things and lifeforms in your room; all of these attain a life of their own as individuated consciousness of yourself. I am spinning and weaving webs in all of the corners to eventually encompass your entire room and everything within it. As you are here in your favourite place; the other rooms in your house can become mirrored in this one and I do not weave in every room, just the one which you occupy.

The weaving of the web of life so unifies all the things of you, you have given away to create your environment to live in.
In some way, all the things which are trying to run away from you to be separated from you as their life-giving goddess; cannot do so and become trapped in my encompassing web.
But this serves a deeper purpose too. Your entire room will become a cocoon for your graduation from April, the goddess in mirrorland to April, the goddess in mirrorland and in wonderland simultaneously'.

'But I can never get into wonderland, except going backwards and in trying that I hit my head against the glassy wall of the mirror', April protested.

'I have a surprise for you April', replied Grandma Spiderwoman.
'You know the web I have spun over there in the other corner; go there and look what is there dear one'.

April went to the other older web and peeked through the webby texture.
There from an egglike construct emerged a snout, followed by a fishlike creature.
'Wow', said April; 'I have discovered a dolphin in a segregated place in my own room.
Hi there dolphin; I shall name you Cinderella, Cindy for short; because you have given me new joy after awakening like snowhite from a peaceful slumber'.

'My pleasure to meet you April'; said Cindy the Dolphin. 'Yep, I am indeed another goddess, who has chosen to play with you in your universe. Do you know what my coming out of this cocoon signifies in the magic of things'?

'No, Cindy', said April; 'but Grandma has said, that this entire room will become such a cocoon. But why do you call my room the universe; there are many other rooms in my house as the original room? This is just my special room as part of my house. I know that my house is the universe, Mac the Knife has said so and so has Brooke my Cat'.

'Ah yes April', said Cindy 'and your Grandma is very wise indeed. She really knows what is going on and she is that old wisdom part of yourself, which you have allowed to externalise relative to yourself from deep within, your inner knowings.
You see, the spinning of the web partitions your special room as an inside and an outside. Without the web, your special room is a holographic image of the universe as part of your house. So subdividing your special room partitions your local universe once more, say into the hologram of your special room becoming a planetary environment as within the web and an extraplanetary or galactic environment outside of the web'.

'Ah, I get it', said April; 'and because you have come from behind the web, you have also now come from the extraplanetary environment of the galaxy this planet is a part of'.

'Yes my sister and now you might understand the wisdom of the elders. They know of the galaxies and the partitionings of the holography. April do you wish to visit your own galaxy'?

'Of course Cindy; are you suggesting we can travel to the place in the galaxy from where you came from as a goddess now incarnate in my room'?

'Indeed April, this is what this web implies if spun comprehensively.
As the corner of this room is covered in the form of a triangular prism of four faces and as your room is a spherical mirror containing your room in the geometry of a cube; you can topologically transform the geometries any way you like for a given volume of the space defined by this room.
Then spinning the web more and more and in letting the four corners converge, will define your holographic universe with you being its center, no matter how you have partitioned yourself to create your own environments'.

'What is the geometrical shape of the web before you dear', the sound of Mac the Eagle interrupted? He had suddenly materialized at the left side of April talking to Cindy.

'Ah, wait let me see. It's an equilateral triangle Mac the Knife', April replied.

'Indeed, and the vertices meet at one of the corners of the cubical room to form a triangular pyramid as a trirightangular tetrahedron', Mac the Eagle continued. 'This rightangled tetrahedron, constructed from three rightangled isoceles triangles and one equilateral triangle is closely related to the  tetrahedron as a regular tetrahedron of four such equilateral triangles in the minimum spacial configuration to create a 3-dimensional space in the intersection of 4 equidistant points. This is known as the Tetractys of Pythagoras.
Furthermore this tetrahedron is dual to itself in that its mirror projection through its center creates a Stellar Octahedron whose combined 8 vertices become the corners of a Cube. Then the inside of your cube contains a central Octahedron, another Platonic Solid of which there are precisely five as convex regular polyhedra; namely the Tetrahedron, the Cube, the Octahedron, the Dodecahedron and the Icosahedron. Mother Nature favours the symmetries of those Platonic Solids over all else, due too the mathematical fact that there exists a special geometry based on fivefoldedness, which minimises the expenditure of energy in compressing information as a form of physical consciousness residing in the geometry of space. You can term this the "packing efficiency" of Mother Nature's data. Do you understand this April'?

'Not really Mac', replied April; 'you are using some words I'll have to talk with my friends Brooke the Cat, Billy the Terrier and Cindy the Dolphin about. But yes I see the equilateral form of this web of Grandma Spiderwoman and as Cindy said; configuring the spherical volumes with the cubical volumes will allow to generate such a harmony in the outside communicating with the inside'.

'Yes April and so the entire volume of your universe can be said to be quantized and made up of either vertex-oriented Platonic Tetrahedra in a computational manner or as some sphericity associated with the minimum mass counter N which Brooke has mentioned before as information from her sources - my brothers in the natural philosophers. But I shall exposit on this at a latter time; may I take my leave now dear, I have some business to attend to in regards to another goddess student and her beau, both friends of mine in my universe. You will find them as part of your universe as Caroline the Ibis and Herbert the Yeti'.

'Sure Mac the Knife', said April. 'And I do hope to meet your friends in my universe very soon. This sounds interesting, the concubine of the Yeti as a mythological creature, also known as the abominable snowman is the bird of wisdom of the nile'.

And as he had appeared, Mac the Eagle disappeared and April looked at Cinderella.  

'So all we have to do is move behind the spun web in this corner and we will change the planetary environment into a galactic environment', asked April.

'Yes April, so all you need to do is step in and off we go', nodded Cindy.

As April touched the spider's web, there was no resistance. It was like the entry from wonderland of April's birth into mirrorland - effortless.

'How do we choose to travel', asked Cindy? 'We can watch this computer screen here in a kind of simulation or we can use some contraption like a spacecraft to travel in the hologram to my "special room" as the goddess Cinderella on a planet called Akashia orbiting a star named Sirius aka Isis-Sothis'.

5. April meets Grandpa and peeks into the far future in the age of the universe 

One morning April decided to ask Grandma about Grandpa. April had wondered about Grandma Spiderwoman's partner, but the last time April wished to ask Grandma, Grandma had begun to weave the second web in another corner of April's room and leading to the meeting with Cinderella, the Dolphin.

'Grandma, where is Grandpa', asked April, musing over the ever increasing complexity appearing in Grandma Spiderwoman's second spun tapestry?

'Oh, April, your Grandpa is rather engaged at the present time. He is preparing your house for transformation from the outside, just as I am preparing the renovations from the inside.
I am afraid, you will not be able to see Grandpa for a while; but you might be able to converse with him over the conduit to the outside, the little window in your special room through which you can see the far away mirror'.

'Wow', said April. 'I thought the entire universe is mirrored in my house, just as I represent all the matter within it. So in sharing my weight, this my house became redesigned in a distribution of my material beingness. This has to do with those galactic seeds, Brooke my cat has spoken about.
How then can Grandpa be outside of my house? You as my Grandma are part of me, as you yourself have said'.

'Well my dear, this is part of the greatest mysteries of them all and you will receive the answers in due time. But knowing Grandpa, as I do, he would, should you be able to talk to him, be able to perhaps give you some hints in a way you can understand now on the path of your life into a deeper comprehension of the partnership between wonderland outside and mirrorland inside.
But I can tell you, that Grandpa is as much a part of you as I am; we are your grandparents after all and so in some way we gave life to you, but you also gave life to us. One day you will understand this in a unique kind of wisdom, which can only be found in mirrorland'.

'Hmm, so my reason and purpose for being in mirrorland is to connect mirrorland to wonderland.
This would account for your separation from Grandpa on the inside with me here in mirrorland and his being on the outside in wonderland'.

'Yes April, this is true, but Grandpa himself, whilst being outside of mirrorland is not in wonderland. He also is in mirrorland, but not like we and your friends are. But he should explain this to you, as he has a different perspective on the situation from where he is. Should you try to discern yourself in the far away mirror, Grandpa might show up. He requires concentration on the selfperception to be able to communicate to the inside from the outside'.

'This is very intriguing Grandma and I shall try to talk to Grandpa about it'. April took her leave and proceeded to the little loopey window in her sanctuary to again discern the far away mirror and her image reflected there.

The more she attempted to discern her image in the distant mirror, the more mentally tired April became. 'I am getting a headache', April thought, 'and Grandpa must be busy. He doesn't seem to notice my concentration and intent'.

April decided to give it a break and have some Italian coffee to wake herself back up.
April had learned to manipulate her environment and to engage with herself and her many friends in some experiential manner.
To keep herself occupied, April had developed interactions with things and living beings; engaged in talking to herself and to the things and friends in whatever way seemed appropriate and instilled in April a sense of fun, learning and the gathering of experiences through her imaginative creativities.

'Hah, I have become my own data collector', April often mused. 'I want to find out what this life of mine is all about as an individuated goddess from wonderland, where all the goddesses are as One'.

Stimulated by the caffeine of her Italian coffee; April returned to the loopey window as her doorway into another world, the outside world into the greater universe as the space between the far away mirror and the mirror in April's house, the one through which she had entered mirrorland from wonderland.

'Make yourself comfortable April'; a firm, yet gentle voice suddenly entered April's mind.
'I have heard you before, my princess, but I would prefer you to talk to me in comfort and not under stress and tension or in suffering duress in just conversing with me.
You shall not be able to see me, but my nature of being outside of your universe does allow us to speak to each other from a secondary mode of communication, that of the sunbconsciousness'.

'Oh, I am so happy I can talk to you Grandpa', April laughed. A great weight had fallen from her shoulders, now that contact with Grandpa had been made.
'So you can talk to me and I can hear you because we are on some subconscious level'?

'Yes April. The way you talk to Grandma is the tertiary level of the waking consciousness. There is a primary mode of the superconsciousness and it is that mode, which directly connects wonderland to mirrorland'.

'Grandma said, that you are not in wonderland, but in mirrorland. How can that be, as you are communicating in the secondary mode', asked April?

'The far away mirror is the doorway or portal into wonderland April', replied Grandpa.
'I am literally located in between those two mirrors, yet in the same dimension of that in which you are experiencing within your house. Then the entire universe as your house is mirrored relative to itself as from within, but also relative to itself as from without.
Remember that your friend Mac the Eagle has hinted as to the importance of the creation of this far away mirror to discover the measurement of distances in the expansion of your universe.
I know, that Mac the Knife has the detailed information for you to understand the size and age of the universe and the scale relationships of those metersticks, the metrics.

But I can tell you, that this far away mirror limits your 3-dimensional universe just like an acorn or a mustard seed does.
A little seed is planted and then breaks open to disperse the, say genetic information, contained within. This genetic information, say of the acorn, then builds the shoot of an oaken tree and which then evolves over a suitable period of time into a majestic oaken tree on whom then wise owls my ponder the stars and upon whose branches nightingales may then sing their songs to the moon.

The oaken tree is your house April. But is there not a sky above the oaken tree and a ground beneath, even its far reaching roots?
Now my dear, can you imagine the oaken tree all unto itself; there is no sky above and no soil below?
You cannot do so because you know of the sky and the earth; but if you return to the seed before it sprouted; you can envison the whole tree in its acorn'.

'Oh, I see Grandpa', said April. 'The existence of the oaken tree is a kind of time travel. It is born from a preprogrammed genetic information; which knows how to build the tree.
So the oak is born from the preprogrammed information to gather the experience of the being, the environmental interaction and then after some time; the oak gets too old to support its preprogrammed structure and it withers and falls, recycling its material essence'.

'Well realised Apri'l, said Grandpa. 'Then the collected life-experience becomes a new seed, for a new acorn, despite the earlier material of the body of the oaken tree dispersing.

Well, dear I shall allow you a little peek into the far far away future. You will have to gather much more background information to understand what I shall outline to you. Mac the Eagle will give you more information about the cosmology, the lightpath and the distances and the timescales of the universe. Your other friends of the natural philosophy will also share ideas and data with you and you with them; and then you might remember some of the things I told you and then this somewhat hard to process information might crystallize in your understandings.

The 3-dimensional universe you live in is not only multidimensional, but extra 3-dimensional. This means that the 3rd dimension is both limited and unlimited. It is limited as a seed for higher dimensions and unlimited in intersecting the 3rd dimension in multidimensionality.
The energy for the birth of your universe is similarly limited and unlimited in the seeds and the seeds of the seeds.
This is called the Arrow of Entropy and the Arrow of Time by the natural philosophers. Some of the 3-dimensional scientist think that those arrows are onedirectional, but they are only in the individual seeds. As soon as a seed's energy has dispersed to a certain degree in a time period of about 4,000 billion years, the old seed sprouts a new seed, which builds upon the dispersed seed as a new seed.
The far away mirror is just the limiting parameter for the first and initial seed to begin its dispersion. This limiting parameter is about 17 billion years and so it takes about 236 "heartbeats" or "breathing cycles" for the 3-dimensional universe of your house to sprout its newness from its oldness.
This does not mean, that this, your house will disperse into nothingness. This your universe will remain as the seed of the 3rd spacial dimension for the seed of the 4th spacial dimension.
Whatever is seeded beyond this far away mirror is also reflected back into the primordial seedling, this your house.
In this way the limitation becomes delimited and the boundedness becomes unbounded in another greater or higher dimensional boundedness and so on.

But in 4 trillion years, the energy in your universe will have dispersed to require a recharging from wonderland. You April, will have given so much of your weight away and you will have gained so many friends; that you simply have to build a bigger house to experience it all.

The energy of the mirrorland derives from wonderland and the cosmological terms describe this in the duality between the Oneness of the Universal Goddess and the Manyness of the Individuated Goddesses.
The technical term is temperature and where this temperature is not the parameter of the kinematics and the inertia, but a temperature of noninertia, also labelled as the gravita of monadic superstrings.
For energy to exist in whatever form, say that of the thermodynamic universe of expansion and of entropy as the dispersion of energy; the antistate for this energy must also exist.
In due course you will understand, that the antienergy resides in wonderland as Alice, the Shadow April and mirrors the energy of April, the Shadow Alice in mirrorland.
The antienergy in wonderland is precisely equal to the energy in mirrorland, but only from wonderland can the energy in mirroland become supplemented. Many natural philosphers know this as the closed system of your house and attempt to reduce everything in your closed system to some elementary beginning or starting point. They have encountered a lot of problems in doing so and some have invented ever more elaborate models to explain mathematical singularities of the beginnings, the Big Bangs and brane collisions and so on.
The simple solution is not to forget wonderland, as with wonderland, the "many worlds" and the multiverses are naturally contained within the greater universe. There are many mansions in mirrorland, April, as you surely will find out for yourself one day, if you have not already done so.

You may meet another friend of yours one day on your journeys. This friend is a part of your weight and he is Johnny Lately the Mathematician; who knows about the special Gaussian Wavefunction descriptive of your house. This wavefunction descibes the connection between the finiteness in mirrorland and the infiniteness in wonderland, finitely reflected in the Riemann-Zeta Bound of the "frozen spacetimes".
 
The loopey window you are looking through is the metric of the gravita and it also is the metric of the far away mirror.
When your house had reached halfway the distance to the far away mirror in the expansion of its metersticks so 2.2 billion years ago; then the limiting parameter of the 3-dimensional seed was activated.  
When your universe was born, it was the monadic noninertial temperature, which created your house as the boundary for you to later throw your weight around in the distribution of inertia.

You may ask certain questions, like "How old am I as the Universe" and this is a very good question at the core of all cosmology.
You will find, that your house has four different metrics and so there are four ages and four sizes for your universe and depending on your viewoint of observation.
Your house as measured from within has the volume of a sphere, but measured from my location, this volume transforms into a special toroidal shape, like a doughnut without as hole.
This then gives the volume V₁₀⁺=2π²R_max³[n/(n+1)]³  for an inertial doughnut age of 8.96 billion years or a 15.03 billion year spherical age. These are the Actual Inertial Ages for your universe as envelopes or upper bounds and these are not the ages as measured by your natural philosophers.
The transformation factor between the "doughnut without a hole" and the sphere is the upper bounded Chaos Constant known as the Feigenbaum-Delta: σ_Fmax=3π/2.

Should you measure your universe from the position of wonderland however, the volume increases due to the 4-dimensional seed activated by the 3-dimensional seed.
Technically the surface on which the far away mirror exists becomes a 3-dimensional mirror just as the location of your loopey window is located on the inside of a spherical 2-dimensional mirror.
Then the outside of your loopey-window surface changes from a spherical surface to a doughnut surface, remaining however 2-dimensional, albeit in transition to 3D, obtained at the far away mirror, not asymptotically, but gravitationally through the monadic gravita.

Outside the far away mirror then the surface topology is 4-dimensional as the orthogonal vector nR_max in the expression dV₁₁⁺=S.dR=2π²R_max³dR from V₄=½π²R⁴ and dV₄/dR=2π²R³

The extra-3D-volume so becomes:  V₁₁⁺=n³2π²R_max³ and is measured relative to your inside as an age of 32.04 billion years, but relative to my outside as 19.11 billion years. These are the Actual Electromagnetic Ages for your universe.

The Measured Ages for your universe are however lower, than the Actual Ages, because of the intersection of the 3rd dimension with the 4th dimension.

If the critical volume is defined as V_critical=2π²R_max³, then the extra 3D volume expanding as a 4D volume seed will be V₁₁^-= n.V_critical  and as reduced from  V₁₁⁺=n³.V_critical
The Measured Electromagnetic Age for your universe then is 17.62 billion doughnut years and 29.53 billion sphere years.

The following expressions must hold and define the multivolumes in labels, which can then become reinterpreted in the form of 'missing energy' and 'missing mass'. Many cosmologists in your universe term this the search for 'dark energy' and 'dark matter' respectively.
 
Multidimension Factor:  DIM      = V₁₁⁺/V₁₀⁺ = V₁₁^-/V₁₀^-
Dark Matter Factor:      DIM_DM = V₁₁^- /V₁₀⁺=(n+1)³/n²~7.561
Dark Energy Factor:      DIM_DE   = V₁₁⁺/V₁₀^-=(n+1)³.n²~12.434

You so must have a reduced 3-dimensional inertial volume V₁₀^-, which is given by 
V₁₀^-=(n/[n+1]³)2π²R_max³  and provides a doughnut age of 8.26 billion years and the age measured by the astrophysicist in your house, namely 13.85 billion years as the Measured Inertial Ages for your universe.

Comprehensively then, April, your present universe is undergoing an ongoing transformation. You might term it the seeds are sprouting for the harvest and the harvest are the seeds from the seeds and the harvester is you in Oneness and in Manyness'.

'So this is why Grandma is weaving those webs', interjected April. 'She mentioned this preparing of some cocoon'.

'Do you think you are a beautiful goddess, April', asked Grandpa?

'Well, yes, Grandma also said that the far away mirror shows the most beautiful as the oneness of all the individuations', replied April.

'This transformation of the blossoming new seed from the old seed will render you even more beautiful, than you are now', giggled Grandpa.
'Compare yourself to your companion and friend Scott the Caterpillar, April. Like you he will become cocooned in his house and the one you share and like you, he will one day remember wonderland and in an appropriate utilization of the far away mirror; both of you shall metamorphose into the Butterflies of Dragonia as the Butterflies of Serpentina of the extra 3-dimensional reality and much closer to wonderland than mirrorland, yet still part of it.

I say, this is enough information for one day and I shall leave you to your comforts now, concluded Grandpa'.

'Thanks for this information Grandpa', said April. 'Yes, I certainly have something to think about and to discuss with my friends. So Scott the Caterpillar and his house is also in transmutation and his house is my house through our partnership with each other; I'll get this.
But Grandpa; I know that Grandma is engaged in my special room of the planet Gaia and that Grandma is like an ambassadora for my sanctuary Arachne de Gaea' Do you have a name and a "special place" too'?

'Yes, my dear granddaughter, I do have a name and my abode is the outside of the inside of Arachne de Gaea.
It is called Draco de Uraeus and my name is Grandpa Serpent-Man.
I am a fiery dragon from Plato's Land, flying about just outside your Cave of the Shadows.

6.
 

Now this scalefactor R(t)=a.Ro means that some 'size' of the universe at time to was characterised by the scale Ro, which has a, called the expansion parameter, naturally getting bigger in time.

But what about this original size of the universe Ro?

Contemporary cosmology says that Ro was the size of a 'grapefruit' and has now grown to the size of the Hubble radius of magnitude between 10 and 20 Billion lightyears.

Now the expansion parameter a does indeed increase as we shall show, but the Ro is actually a maximum size, which R(t) is increasing towards asymptotically in an oscillating series expressible in the sequence 0/1, 1/2, 2/3, 3/4, 4/5,...,n/(n+1) thus eternally approaching but never reaching unity 1.

So the contemporary model is mathematically correct, but then begins to assume the Hubble Relation to DECREASE in the H=a(dot)/a definition as a constancy, albeit epoch dependent.

If a increases, as it must, then a(dot) must increase in the same proportion for constant H(t).

Equation (1) then says that a(doubledot)/a=-4G/3{+3p/c^2}/H^2=deceleration parameter q........(1*),

because differentiating a as dimensionless fraction for the expansion of scalefactor R(t) with respect to time t is a(dot)H and differentiating again for acceleration is a(doubledot)H^2 for the correct units for acceleration in displacement per time squared.

q=-(a(doubledot)/a)/(a(dot)/a)^2=-a(doubledot)a/a(dot)^2=(nps)/(Rmax.fps^2)=GoMo/(c^2.Rmax^2) and qo=Mo/(2Mcritical)=o.Vo/(2critical.Vmax)={4Goo/3Ho^2}(Ro/Rmax)^3..........(14)

Then the standard cosmology reappears in distributing the density o(Ro/Rmax)^3=+3P/c^2, that is

Pressure P=(c^2/3){o[Ro/Rmax]^3-},

P=0 for o=given by the mass seedling Mo and the Omega of 0.028=2qo which assumes Ro=Rmax in the superposed curvatures of the boundary conditions =0,1.

So we see that the Lamda Quintessence is incorporated into standard cosmology as the evolution of the universe bounded in its curvatures.

This means, that the evolving cosmology uses a negative hyperbolic curvature for a open universe, yet bounded in its asymptote of =0 for the expansion parameter a=n/(n+1) approaching 1 in infinite time t=n/Ho.

This superposes the fixed =2qo for the required Euclidean flatness onto the quintessential  from the inflaton nps=ps/Rmax.

Curvature =R^2{Ho^2+/3-Ho^2}=(aRo/c)^2{Ho^2(-1)+/3} then becomes naturally -1 for =''=0 and Ho=c/Rmax=c/Ro, implying that a=1 that is the limit for =0 and =1.

But this cosmological constant '' is NOT the same as the quintessence and can be set equal to 0 just as originally proposed by Albert Einstein.

The demetricated expansion parameters then become:

a=n/(n+1); a(dot)=Ho/(n+1)^2 and a(doubledot)=-2Ho^2/(n+1)^3.

Now solving qo=/2=Mo/2Mcritical=0.01405.. DEFINES no=qo at redshift z=7.477 and gives in the definition of (14) q(n)=2n; (generally for n=a/(1-a), (aq(n)=2 for a=X for the acceleration redshift discussed later).

So q(no)=2qo=2no=o for a radiation dominated universe with =3P/c^2 and as the boundary condition for the superposed curvatures.

The deceleration parameter of the standard cosmology so defines this limiting threshold between a radiation dominated universe with qo=o and a matter dominated universe for which qo=o/2.

q(n)=2n and q(a)=2a/(1-a) the latter function increasing q by 2 for any half-cycle Hubble Oscillation.

q(0)=0; q(1/2)=2; q(2/3)=4; q(3/4)=6; q(a=n/(n+1))=2/(1/n)=2n.

Now this shows that for any n >1/4 the universe exceeds the threshold q(n=0.25)=1/2 and the standard cosmological parameter begins to diverge from its stationary value qo.

n=0.25 defines a universe of age 1/4Ho of so 4.225 billion years and at a recessional velocity of (16/25)c for which a 64% (v/c) ratio implies a cosmological redshift of z=Sqrt(1.64/0.36)-1=1.13437...

This indicates the 'acceleration' scenario manifested at n=0.618..so 6.23 billion years from the qo-threshold and so 8.67 billion years in the past.

The standard cosmological equations then are solved in writing R(doubledot)=a(doubledot)Rmax

or R(doubledot)=-GM(R)/R^2 +Q(n), where Q(n)=Q(R/(Rmax-R)) via R(n)=Rmax(n/n+1).

-2cHo/(n+1)^3=a(doubledot)Rmax=-(4(n)G(n)/3)R(n)+Q(n), considering the distribution of densities and limiting value for the deceleration parameter q as discussed with Q(n) forming the quintessence as Q(n)=Q(a/(1-a)).

This reincorporates q but not as function of the Hubble-Law.

Rather it uses its limit in the curvatures and in  and incorporates  in the form of a(doubledot).

-2cHo/(n+1)^3= -(4G(n)/3)(3M(n)/4R(n)^3)(R(n))+Q(n)=-G(n)M(n)/R(n)^2+Q(n).

It is not required to solve for the expansion parameter as a function of n, but one can solve for the Quintessence Q(n).

It can be shown, that M(n)=Mo.Sqrt{Y^n} and that G(n)=Go.X^n with X=1/Y as pentagonal symmetry parameters of the cosmogenesis.

It is then evident, that the demetrication of the General Relativity parameters in dimensionless cycletime n not ony defines the expansion parameter a, but also redefines the Hubble Law in its boundary conditions.

Now in Quantum Relativity, Ro=Rmax and a=n/(n+1) defining the series above as a sequence of the expansion parameter over time, which becomes demetricated in parameter n=Hot.

Then R(n)=Rmax(n/(n+1)) and a(dot)=Ho.Rmax/(n+1)^2 with a(doubledot)=-2Ho^2.Rmax/(n+1)^3.

But HoRmax=c and the metricated acceleration parameter in General Relativity becomes reformulated as demetricated a(doubledot)=-2cHo/(n+1)^3 in Quantum Relativity.

The equation for dynamical motion for the universe then becomes in General Relativity:

a(doubledot)/a = -4G/3{+3p/c^2} and -2cHo/n(n+1)^2 in Quantum Relativity for a zero cosmological constant.

Integrating a(doubledot)/a via acceleration A=vdv/dx=d(v^2/2)/dx with respect to time and for r=aro and r(dot)=a(dot)ro and r(doubledot)=a(doubledot)ro and M=V=4r^3/3 gives:

r(doubledot)/(r)dr=GM(r)/r^3)dr and d(r(dot)^2)/dt=2r(dot)r(doubledot)=-2GM(r).d(1/r)/dt=2GM(r)r(dot)/r^2.

As r(dot)^2=a(dot)^2ro^2=2GM(r)/r -c^2, with constant of integration ro(dot)^2=a(dot)^2ro^2=-c^2.

Hence [a(dot)/a]^2=2GM(r)/(ra^2ro^2)-c^2/(a^2ro^2)=8G(r/aro)^2/3 -{c/aro}^2=8G/3-{c/aro}^2...(9).

Now deceleration parameter q=(a(doubledot)/a)/H^2=(4G/3)(+3P/c^2)/H^2 with H^2=8criticalG/3 and so as =critical q=(/2)(1+3p/c^2), showing that for a flat universe, =1 and q=1/2 for p=0.

Equation (9) simply adds /3 as the 'cosmological constant', which if large overpowers the other terms in

a(dot)/a=Sqrt(/3) for a(dot)=a.Sqrt(/3), which on integrating da/a=Sqrt(/3) yields ln(a)=Sqrt(/3) and the exponential evolution of a(t)=exp[Sqrt(/3)t.

(-8p　

We shall then find that the relationship between Ho as the nodal Hubble Constant becomes the proportionality constant for the changing Hubble-Constant as a function of parameter n.

Specifically the timederivative of n is Ho in dn/dt=Ho and n can be said to be the dimensionless tau-time in General Relativity (GR), which allows the partitioning of the derivatives as chains.

Example (actually used in GR):

Acceleration a=dv/dt=dv/dx*dx/dt=v*dv/dx=d(v^2/2)/dx.

This eliminates time in the acceleration parameter and represents acceleration as a function of displacement x.

Considering the universe to be a summation of density states of pressure p and density then we rewrite the Raychaudhuri equation:

Acceleration dR^2(t)/dt^2 = -(4GR(t)/3)+3p/c^2

Now we can relate the 'Equation of State' in the relationship between mass-density and pressure p via the summation of the parameters enclosed inas say dimensionless integer states.

=Mass/Volume and p=Force/Area=Energy/Volume so (M)ass*p=(E)nergy* or Mp=Mc^2*

The Equation of State is then w=p/c^2.

For relativistic matter and radiation w=1/3 and for nonrelativistic matter and radiation w=0. This indicates that the pressure p=0 for any density considered in the invariance of lightspeed c, that is demetrication.

What does this mean?

It means that an universe subject to its own boundary condition (the lightmatrix as the aether of continuity) is nonrelativistic as a 'cosmos of light'.

This is the modular duality of the 11th dimension of the superbranes.

The universe in 11D then never changes its own invariant matrix parameter of invariant c.

This is precisely the postulate of Special Relativity and can so be seen as a direct consequence of Quantum Relativity as the Demetrication of General Relativity using Special Relativity in the process.

The 11D universe is 'Steady State' in encompassment of the lower dimensional universe, subject to the pressure variations and the velocities of inertial objects upper bounded in the invariant 'c'.

The modular duality then allows a minimum frequency to be be in c-proportionality to a maximum frequency.

This minimum frequency is the nodal Hubble Constant Ho and the maximum frequency is the frequency as embodied in the volume-invariant Weyl-Tensor and denoted as fps.

The invariance of the relativistic cosmos is then given in the identity (of superbrane parameters):

c=ps.fps=Rmax.Ho or Ho=c/Rmax...............................................(4).

Now Rmax is simply the limiting R(t) in GR as the scalefactor said to be taken as unity for the Hubble-Epoch.

So GR uses the ratio R(t)/Rmax or a/ao as the scale factor for cosmological distances.

But the 11D cosmic 'steady state' represents the electromagnetic universe, always travelling with c-speed in cycles of expansion and contraction.

That means, that the universe oscillates between even nodes as defined in maximum frequency fps and odd nodes defined in minimum frequency Ho.

But we shall now return to the metric universe as the complexified 10D universe which does not oscillate but expands asymptotically as required by the critical density critical for the Euclidean flatness experimentally observed.

The informed reader can then witness, how the metric universe in the public realm is simply the consequence of a demetricated universe as indicated in the above.

We begin our demetrication process in proposing the socalled critical density critical for a perfectly flat Euclidean universe to be embodied in the equation of state.

We then rewrite (1) as -(4GR(t)*critical/3)(1+3p/critical*c^2).

Conventional (nondemetricated GR) then derives this critical density in differentiating between the summation of density- and prressure states in partitioning the Raychaudhuri expression into its density part (2) and pressure part (3) and introducing curvature k= (0,+1,-1).

v(n)^2/c^2 +k = 8GrR(t)^2/3c^2.......................................................(2) and

2a(t)/a + {v(t)^2+kc^2}/R(t)^2 = -8Gp/c^2..................................(3).

Standard Cosmology now introduces the Omega Factor as the ratio between density i andcritical or =icritical as alternative to the summation states of matter, radiation and the lambda () 'cosmological constant' now said to be 'dark energy'; i.e. total=Mass+Radiation+.

The important point here is, that Standard Cosmology assumes the present scalefactor to be ao as the reference of 'looking back in time' for a Earth-based 'present time'.

The correct scenario is that ao=Rmax IS the fixed scalefactor for all cosmic times given in (linear) time t=n/Ho. Then of course dn/dt=Ho as the odd-nodal and true Hubble constant.

I should say here, that this misinterpreted application of the GR scale factor leads to the 'problems in cosmology' associated with space expansion and the redshift scenarios.

Then the critical density derives from the acceleration coefficient and the incorrect Hubble-Constant definition as 'Ho'=v(t)/R(t).

8critical*GR(t)^2/3c^2 =1 and critical=3c^2/(8GR(t)^2)=3'Ho'^2/8G in assuming that v(t)=c for R(t)=Rmax for a 'present Hubble epoch'.

But this is precisely what I have described earlier as the invariance of the 11D universe.

So in the demetricated scenario we use (2) to show that the 11D universe is simply an encompassing 'Mother Black Hole' of Schwarzschild solution with scale Rmax and critical Volume Vcritical for a critical Mass Mcritical, which AS the critical density renders the universe flat with k=0 and =1; just as required in the Standard Big Bang Model.

Then critical derives classically as Rmax=2GMcritical/c^2 for critical=Mcritical/Vcritical=Rmaxc^2/(2G*[4Rmax^3/3])=3c^2/(8Rmax^2)=3Ho^2/8G by definition of (4).

Equation ( 1*) now becomes deceleration parameter q=(1/2critical)(+3p/c^2)=(/2){1+3p/c^2}.

This means that q=1/2 for a matter dominated universe with pressure p=0 (or small) and that q=1 for a radiation dominated universe =3p/c^2 because the equation of state defines w=1/3.

The basic Cosmological Equation incorporating the curvature k becomes then:

R(dot)^2 = 8GR^2/3 + R^2/3 - kc^2

k=Ho^2[o^2-1]+/3]/c^2.

So k=0 for =1 and =0 and k=1 for =1 and =3 and k=-1 for=1 and =-3 for a mass dominated universe of the Friedmann-Lemaitre solutions for the Einstein Metric

ds^2=

Next the flatness of the universe is the ASYMPTOTIC boundary of 11D, allowing the oscillating electromagnetic universe to form the 'aether' for the 10D universe.

Please note, that a 10D universe is a 4D universe with 6D congruent with the spacetime of the relativistic Minkowski-Einstein-Riemann spacetime.

It is known as the Riemann Hypersphere or the Poncare 3-Sphere topologically.

So while I often mention the 10D universe, there is nothing 'hidden' just multivalued parameters because of the freedom degrees represented by volumes containing scaled subvolumes and the like.

3 Degrees of translation become multivalued in 3 degrees of rotation (each about one of the translations, say XYZ) and then in 3 degrees of vibration for a 9D 'spacial'or volumed cosmos.

Then linear time becomes the 10th dimension for the metric universum.

Modular duality introduces nondimensional cycletime n and 3 degrees of quantisation for a 12D continuum in which the 12th dimension accomodates the EXPANSION of the Rmax Limit into the undefined 'void' becoming defined and is imaged in the 11D of the 'Witten Mirror' then being the 10D of the asymptotic spacetime which does not exceed Rmax because of the c-invariance.

Furthermore the curvature k is now found to be multivalued.

Euclidean flatness implies k=0 for the asymptotic expansion and the =1.

But we also now know, that the universe is closed in 11D and open in 12D, 12D (the Father-Space for the Mother-Space Black Hole to expand into).

So the positive curvature k=1 depicts the electromagnetic universe superposed onto the 10D asymptoticone and imaged in the negative curvature of k=-1 as the 12D/10D mirror mapping.

We now simplify (2) to formalise this as the reformulation of the Hubble Law.

The asymptotic expansion is given by the demetricated scale factor R(n) as a function of the cosmic nodal frequencies or Hubble Constants from maximum fps= to minimum Ho=c/Rmax.

So scalefactor a=R(n) describes a decreasing curvature from metric maximum warpspace given by wormhole wavelength ps to the asymptotic bound of Rmax.

An expression for R(n)can be derived a number of ways, but is based on the definition for the natural exponent 'e'=limit[n->Infinity] {1+1/n}^n; the derivative of the basic exponential function being itself of course in d(e^x)/dx=e^x.

R(n)=Rmax{1-n/(1+n)}=Rmax(n/(n+1)) is the result.

Now recall the dimensionless nature of n=Hot which so demetricates all of GR in substitution R(n=Hot).

We have elimninated linear time in analysing the universe as an oscillating wave in 11 dimensions.

Then the position of the evolving 10-dimensional universe is a function of the nodal frequencies and the scenario of the expanding universe into the void becomes one of an oscillating universe with precise boundary parameters.

The n-derivative for this displacement of the scalefactor is simply V(n)=dR(n)/dn=Rmax/(n+1)^2.

To reclaim the linear t-parameter, we partition the derivative as V(n)=dR(n)/dt*dt/dn for v(t)=dR(t)/dt.

Then V(n).Ho=v(t)=Ho.Rmax/(n+1)^2=c/(n+1)^2, as required by the definitions.

In (2) we so write the Special Relativity ratio v(t)^2/c^2=(dR/dn*dn/dt)^2/c^2=(dR/dn)^2*Ho^2/c^2=(dR/dn)^2/Rmax^2.

So the reader sees, that the velocity units depending on time have become swallowed up in the demetrication of cycletime n in scale factor R(n).

We now proceed to relate v(t) to v(n) in finestructure and definition of R(n), thus finding explicit expressions for the Hubble Constant as function H(n).

H(t)=v(t)/R(t)=Ho*Rmax/{(n+1)2*R(n)}=Ho*(n+1)/{n(n+1)^2}=Ho/T(n) where T(n)=n(n+1)............(5).

Thus the function T(n)=Ho/H(t) redefines the Hubble Law and is bounded in the nodal frequencies.

T(n) is simply the EXPANSION PARAMETER denoted as 'a' in the standard cosmology and a(dot) there becomes a(dot)=(da/dn)(dn/dt)=Ho/(1+n)^2 with the Hubble Law as v/(R(n)=a(dot)/a=[Ho(n+1)]/[n(n+1)^2].

At the Beginning of SpaceTime, the time to (say) specifies the maximum Hubble-Constant as fps.

This is termed the timeinstanton of Inflation and also defines the eigenfrequencies for all mass/inertia parameters in modular duality as the inverse time-frequency modulation.

To derive H(to=1/fps), we simply use our definitions n=Hot and R(n).

H(to)=Ho/[nps(nps+1)] where nps=min/max=ps/Rmax ratio of R(n) in the nodes.

So H(to)=Ho.Rmax/[ps(ps/Rmax+1)]=c/ps=fps in the limit of nps->0.

This limit condition is satisfied in superbrane parameters as it is found that Rmax=1.596..x10^26 metres* and ps=10^-22 metres* for nps=6.265...x10^-49 dimensionless.

This eliminates the 'dreaded singularity' in General Relativity for the infinity reduction of physical quantities, such as pressure and density and temperature.

The infinite asymptotic approach for the 10D universe would of course diminish H(t) linearly to 0 for n approaching Infinity in T(n)=n(n+1).

This is simply the modular duality between the mathematical inversion properties relating 0,1 and Infinity.

Our velocity v(t) relationship is then simply v(t)/c=R(t)/(Rmax*T(n)), that is the linear recessional velocity v(t) defined in the relativistic redshift (z) formulation (6) is v(t)=c*R(n)/Rmax*T(n)=c/(n+1)^2 as required.

The cosmological redshift relation is: 1+z=Sqrt{(1+v/c)/(1-v/c)}....................(6)

Using (6) and the insights of section 1., we can see that the universe is a scaled universe of basic simplicity.

Whilst the mathematical formalisms of the partitioned universe are formidable, its basic geometrical nature should be comprehensible by the scientific novice.

We particularly note the importance of the v(t)/c velocity ratio of Special Relativity.

It is ubiquitous in cosmology and is shown to be a binomially distributed in Quantum Relativity as parent theory for both General and Special Relativity.

Our demetricated velocity V(n=Hot)=Ho.v(t)=Ho.c/(n+1)^2=Rmax/(n+1)^2.

In (6) we use v(t)/c=1/(n+1)^2 to calculate the cosmological redshifts.

We see that NO HUBBLE CONSTANT is required to calculate cosmological distances, once the COSMOLOGICAL REDSHIFT, describing the expansion of the 10D universe within its own 11D boundary is known.

The redshift must be z-cosmological and NOT any superposed motion of galaxy, quasar or cosmological object relative to its surroundings however.

The cosmological redshift is a pure interdimensional 'space' parameter, bounded in H(t)=Ho/T(n) as described.

So the simple consequence of the oscillating higher dimensionality is that the asymptotic bound of the n=1 odd node has already been reached 'presently' and defines the half-cyclic oscillation of the Hubble-Universe.

But WHEN is or was the n=1 nodal universe EQUAL to itself?

When did the 10D asymptotic limit COINCIDE with the first full 11D cycle?

This cyclic NOW-Time is defined as about 16.9 Billion years of sidereal measurement.

So it takes LIGHT to travel Rmax in that linear time interval from n=0 (nps) to n=1.

So in 11D the asymptotic limit in 10D is attained in 16.9 Billion years from timeinstantenuity or the 'Quantum Relativistic Big Bang'.

Now the nodal Hubble Constant is Ho=58.04 km/Mpc.s (defined via Ho=c/Rmax) for the linear time t(1)=n(1)/Ho as the minimum frequency and increases for increasing fractional n towards the maximum frequency fps at the odd nodes again.

So the H(t) function oscillates between its stationary values with a present H(tpresent) calculated in extrapolation as so 66.9 km/Mpc.s and supported as average by measurements (which presume the 'constant' Hubble Law and hence show a large spread in the error bars).

But the observed cosmic acceleration has shown that there is something amiss with the standard interpretation and the discrepancy is the relationship between the space-volume expansion as hypothesised and a PREEXISTING higher D 'space' which is independent on the inertial variables, being bounded by the critical density parameters of part 1.

What we find is that the linearity of the asymptotic expansion given in R(n)=Rmax(n^2/T(n)) imposes a restriction on the cycle time n; namely the condition of actually IDENTIFYING H(t)=Ho.

So there will be a special moment in the linear evolution for the universe when the two cosmic eigenfrequency values of maximum fps and minimum Ho become modularly 'averaged' in a Mean Hubble-Constant Haverage.

Recall v(t)/c=R(n)/{Rmax*T(n)} or rewriting T(n)=R(n)*c/(Rmax*v(t)).

So the asymptotic scale factor or 'size of the universe' always less than its maximum becomes 'harmonised' in c always exceeding the 'group'-velocities of the partitioned wavestates and measured as the velocities of the particles or inertial objects.

Also solving v(t) for n gives you the demetricated cosmological redshift relation n=Sqrt(c/v(t))-1...(7).

As v(t)<=c for all (groupvelocities) v(t); n is always positive but allows for a special value somewhere in between the two nodes, i.e. for the n-interval (0,1), mapped as -(1,2) in the full Hubble Oscillation.

H(n=0)=fps and H(n=1)=Ho with H(X)=Ho/T(X)=Ho/(X(X+1)).

Next we unitise H(t)=Ho/T(n) that is we identify H(X)=Ho; a condition requiring T(n)=1=n(n+1).

Solving the quadratic n^2+n-1=0=(n+1/2)^2-1/4 shows n1=(Sqrt(5)-1)/2 as a positive root and n2=-(Sqrt(5)+1)/2 as a negative root with the property that n1+n2=n1*n2=-1.

We so identify X=n1 and Y=n2; with X setting the REAL TIME tX=X/Ho in the 10D asymptotic mass-parametric cosmolology and Y setting the IMAGINARY TIME tY=Y/Ho in its 12D mirror-image in 'OmniSpace'.

We find in Quantum Relativity, that a cosmic wavefunction descriptive of this 'omnispace' is perfectly reflective about a functional Riemann Bound of n=-1/2 and as consequence of normalising the quadratic root identity from above.

But now we know what the special n-coordinate is, namely n=X=0.618033...

Using (6) with (7) we can calculate the corresponding cosmological redshift, which superposes the nodal limits for the 10D universe as its linearised oscillation of the 11D 'envelope'.

v(n1)/c=1/(n1+1)^2=1/(-Y)^2=X^2=(3-Sqrt(5))/2=0.381966011...., meaning that the 'special moment' in the cosmic evolution occurred when the universe of mass and inertia receeded from its own singularity (which is nps as '0' finitised) at 38.2% of matrix lightspeed.

(6) now calculates the PRECISE cosmological redshift as z=Sqrt{(1+X^2)/(1-X^2)}-1=0.49534878...

Setting the displacement of the extrapolated Hubble Constant at coordinate x in (0,1) gives

Haverage=Ho=/(1-X)=58.04 km/Mpc.s/0.381966011..=151.95...km/Mpc.s.

This corresponds to a linear Hubble-Time of taverage=n1/Ho~10.4 Billion years after timeinstantenuity or (19.1-10.4) =8.7 Billion years in the past.

This is the approximation in the standard cosmology for the cosmic acceleration onset, using the incorrect version of the Hubble Law.

It also shows, that the universe is consistently measured as 'too young' with H(t) too big, compared to say nuclear synthesis in the oldest stellar populations. Edwin Hubble himself calculated a Hubble-Constant in the hundreds, using his basic 'galaxies as nebulae' data.

Should the reader consult countless references as to WHEN the universe appears to have begun changing from deceleration to acceleration (observed by analysis of supernova type Ia luminosity curves), then a redshift of 0.5 always becomes the approximate parameter.

Here then I have shown the limit for any such approximations and the point to which all cosmological measurements of increasing precision will converge to.

We now show the Schwarzschild solution to be a direct consequence of the Raychaudhuri equation in the Ricci Tensor of Mass-Density and show how this solution combines the curvatures as described in part 1.

(2) is written as: v(t)^2/c^2 +k=8G*R(n)^2/3c^2 and as the basic solution for the Riemann-Einstein metric.

We now substitute a 3D volume for the density (n)=3M/4R(n)^3 into the RHS of this equation to get 2GM*R(n)^2/R(n)^3c^2=2GM/R(n)c^2.

Then we multiply both LHS and RHS by scalefactor R(n) to get the RHS as the Schwarzschild metric and Radius for a Black Hole (nonrotating and uncharged and as applicable for the universe as a whole).

The LHS becomes R(n){[v(t)/c]^2 +k}=2GM/c^2=RHS...........(2*).

We have seen in part 2. that the velocity ratio of Special Relativity is a key component for the cosmology and can be rewritten as R(n)/RmaxT(n)=1/(1+n)^2.

This allows us to engage the modular duality in the inversion property, say of the curvature R(n) for the scale factor and its reciprocal 1/R(n) as the curvaturre of the surface.

Equality of R(n)=Rmax invokes the 'singularity' condition at the time instanton nps=ps/Rmax to become the modular dual for the infinite asymptotic expansion in n/(n+1)=1, i.e. n=1+n for curvature k=1 mapping curvature k=0 in the 1<->0 mapping Rmax at infinite linear time onto ps at tps time.

We so map the scalefactor R(n) onto the expression Rmax^2/R(n) in (2*), effectively transforming the velocity ratio term from R(n)^2(/Rmax.T(n)) into R(n)/T(n)^2.

(2*) then becomes R(n){1/T(n)^2 +k}=2GM/c^2..............................(2**)

and incorporates the multiplicity of curvatures.

This transformation then uses the inversion of R(n) in the reciprocal of n/(n+1) as 1+1/n which is the exponential generator.

Our previous redefinition for the Hubble Law at cosmological redshift zHubble=0.49534.. reappears in the form of the 1/T(n)^2 factor requiring to be 1 for the R(n)=Rmax condition of the modular mapping.

Write {v(t)/c}*{Rmax/R(n)}=v(t)/(Ho.R(t)) which, if it equals 1 leads to the 'Restricted' Hubble Law

Ho(t)=v(t)/R(t)={c/(n+1)^2}/{Rmax(1-1/(n+1))}=Ho/T(n).

So the 'restriction' is, that T(n)=1 is the requirement for the Hubble Law to hold.

T(n)=1 for n=X at the redshift zHubble=0.49534.. and Ho=c/Rmax at the even nodes in 33.8 Billion year intervals and beginning at a linear time of n=1 at 16.9 billion years.

SO INDEED, the universe is HUBBLE-ACCELERATING for all epoch (t) dependent Hubble-Constants, using Ho(t)=v(t)/R(t).

The Hubble Redshift implies the Hubble Constant as the HAverage=151.95 in extrapolation for a true recessional velocity of 0.382 c and a true 10D-scalefactor of 0.382 Rmax, which gives the nodal Hubble Constant Ho in unique constancy.

This then shows the 'meeting' between the expanding universe and the recessional 'lightpath'.

Mathematically this is the fact of X^2=(1-X) in the fivefolded cosmological symmetry.

For the Schwarzschild Solution to represent the entire universe we require the Radius R(n)=Rmax(n/(n+1)) to be Rmax and we recall (2**) as R(n){1/T(n)^2 + k}=2GM/c^2...................................(8).

The universe is Euclidean flat for k=0 and Omega=1 which would imply a critical mass density as given in the universe having a total mass of Mcritical=Rmax*c^2/2G=6.47058...x10^52 kg (in superbrane units which also use a varying G constant initialised in Go for M=0 in terms of electric permittivity o, i.e. a quasi-charged but massless universe).

This initialisation defines a corresponding M-seed Mo=1.81371...x10^51 kg.

And not surprisingly, the ratio Mo/Mcritical=0.02803.. which is the Omega for mass as i/critical from part 1.

So anyone can see, that the universe can be closed and Euclidean flat, yet appear to be deficient in mass to ensure the asymptotic cosmos.

This mass deficiency is set by Omega as proportionality and grows in a DIM-Factor defined in the ratio of Volumes in the two Riemann-Spheres describing the 10D/11D interaction.

Since the universe is a 4D Hypersphere of toroidal volume 2^2R(n)^3 in asymptotic 10D as a 3D-Surface and open in 12D with volume n.Rmax^3; this DIM-Factor becomes:

DIM=n(n+1)^3/n^3=(n+1)^3/n^2, calculating for the present n-time as about 7.56.

Then 7.56 10D Hyperspheres 'fit'into the 11D one and the 'missing' mass' or dark matter becomes Omega*DIM=(2.803%)(7.56)=21.20% incorporating the Baryonic Mass-Seed Mo.

Superposed onto Mo is however its 'missing mass' evolution, related by a decrease of the initialising gravitational G-constant value, keeping the productation G(n)mi(n)mj(n) constant for all n via the Euler Identity and the T(n) definitions.

G(n)=X^n.Go and the protonucleonic mass is upper bounded by mc.(Y^n). The Mo/mc ratio describing the number of elementary particles will be addressed shortly.

Then the Baryonic Mass Mo has grown by a factor of Sqrt(Y^n) or Y^ [n/2]~1.3132 for npresent~1.1324..

Omega*DIM*Growth-Factor so becomes the experiemntally observed 21.20%(1.3132)=27.84% of Mcritical.

What is required, is that this Mo itself represents a subset of the Rmax Hubble-Universe in Black Hole equivalence with a Schwarzschild Radius also forming a boundary condition for the asymptotically expanding 10D encompassed by the Rmax in 11D.

I call this sublimit for the demetricated General Relativity the Sarkar Radius, after the Oxford cosmologist Subir Sarkar, who first measured and analysed the large scale supercluster distribution of galaxies and who found a typical scale of about 300 Million Lightyears for them in the late 1990's.

The M=0.02803...then 'closes' the universe as a Sarkar Black Hole with radius RSarkar=2GoMo/c^2 or so 4.4783x10^24 metres, which are so 473.4 Million lightyears.

M=2*Deceleration-Paramerter qo for qo=0.0140 and a Sarkar-'Half-Scale' of 236.7 Million lightyears.

This 'half-scale' relates to the inflation scenario of the Big Bang cosmology, where a phasechange occurred to transform a preGR setting of five demetricated superstring classes into the Einstein Field Equation relating the volume invariant and volume changing (via pressure exerted by mass in the equations of state) parts of part 1.

The precursive energy directly from the superstrings was one of temperature and not of mass.

A 'false vacuum' quantum tunneled as a Temperature Gradient of superstring-tension from the well known Planck-Scale to the Weyl-Tensor scale as given by the maximum frequency fps defined in part 1.

Describing the 'Scalar Higgs Temperature Field' for this superstring tension then shows that the deceleration parameter qo=Mo/2Mcritical=o/2=GoMo/c^2Rmax and thus half the ordinary Schwarzschild metric.

That this is a natural consequence for demetrification can be seen classically in simply equating the Zero-Point-Energy of the absolute Temperature (which is arbitrarily definable) AS a MINIMUM FREQUENCY OSCILLATOR (which the universe IS as a microquantised superstring) with (E)nergy E=hf/2 and setting this as Gravitational Potential Energy E=GMminmmin/rmin for the superstring at the Weyl-Limit referenced by the mass Mmin for the universe.

Then hfps/2=mpsc^2/2=GoMmin*mps/rps and since 2rps=ps=c/fps we have rps=GoMmin/c^2 as the minimum scale for the Weyl-wormhole perimeter and relating a maximum superstring mass mps to a minimum 'macro-Black Hole mass' Mmin (which is half of 12,891.6 kg or so 6445.8 kg).

(There is a minimum superstring mass defined in, what else, but a Planck-Scale oscillation).

The mps-mass is very important too, transforming into the base nucleon mass (proton or neutron) from a later superstring of a different, yet related 'heterotic' class (HO(32)), the Weyl-class being HE(8x8).

This generally becomes the supersymmetric Higgs-Mass-Induction of the lepton-quark families described in the standard model of particle physics. It, needless to say, is the other major part in Quantum Relativity in tandem with the cosmology described here.

But the rps Schwarzschild Solution is the minimum scale for the Sarkar cosmic oscillation, just as it is the minimum scale for the Hubble oscillation.

So for the prudent reader, the asymptotic approach of the 10D universe can be seen to become infiltrated by the Sarkar Oscillation, preventing the Heat-Death' of the entropic universe in a 'running out' of nuclear fuel for the stellar generations of the birth and death of the stars (in the supernovae discussed in the references).

The 'recharge cycle' is found to be so 7.6 trillion years, coinciding with the projected 'heat death' by the way and is a function of the rps-wormhole and Sarkar Radius evolution (described by Strominger branes of extremal Black Holes which become massless as the elementary particles as transformed superbranes).

So the whole universe works in a harmony of modular duality relating its smallest constituents of the superstrings transforming into elementary particles (basically neutrons decaying into protons, electrons and antineutrinos) and its largest constituents, which are superclustered galaxy structures.

But this potential for energy to metamorphose into different forms was born in the gravitational potential of the zero-point-oscillator which is the EpsEss superbrane manifesting the physical universe in the birthing of General Relativity.

Because the superstrings are physical 'singularities', manifesting in the base nucleon, called an ylemic neutron (mass denoted as mc), which is a bosonic dineutron with superconductive properties.

As transformed mps-mass quantum, it gives rise to all the members of the 'particle-zoo' except the gauge-bopsons of the fields for the four fundamental interactions, which derive from a superinteraction uniting the superstring classes.

But relevant to our discussion of GR's demetrication; the Mo/mc mass ratio becomes an important cosmological parameter, because it defines the 'number of elementary particle' making up the mass-seed Mo, thus relating to definitions for the G-constant evolution, which is related to the evolution of the Einstein-Lambda () and so the 'dark energy' for cosmic closure under the curvatures k.

The Raychaudhuri equation (2) is called an 'acceleration' equation and we describe the earliest cosmology in terms of acceleration.

It should be almost self evident, that the decisive parameters for the inflation must engage the 'hyperacceleration' as a function of the Weyl-Frequency fps, acting on the Hubble-Radius Rmax.

This 'de Broglie' matter-wave inflation is simply Rmax.fps=4.793026....x10^56 metres per second as the inflation speed for a 'de Broglie' matter-wave acceleration' of Rmax.fps^2=1.437907...x10^87 metres per second squared.

But this is not the Einstein-Lambda of the 'dark energy', which is (nps)=GoMo/ps^2=2.015..x10^85 acceleration units for R(nps)=Rmax(ps/Rmax)=ps in the 'singularity limit' (see part 1).

So now calculate the ratio of primordial 'dark energy' to 'de Broglie phase acceleration'.

It is (nps)/Rmax.fps^2=0.0140.... WHICH IS PRECISELY THE DECELERATION PARAMETER qo and the half of the Mo/Mcritical mass ratio defining the mass content for the universe for the curvatures.

What does this mean?

It means that the 'false vacuum' for the universe became established in the Sarkar architecture of the sub Black Hole evolution of the superclusters, which REPRESENTS the deceleration parameter and hence the density evolution of the cosmos.

The corresponding cosmological redshift for n=0.0140.. is z=7.477 and represents the largest such redshift any cosmological body (say quasar or Gamma Ray Burster (GRB) can attain.

(8) describes just this.

Rmax{1/T(n)^2+k} for k=0 in (2) must give the Schwarzschild solution Rmax=2GMcritical/c^2.

So { } must equate to unity 1, which it does for our condition T(n)=1 and H(t)=Ho from part 1.

But this could also result in a nonzero k for the asymptotic approach as n tends to the infinity limit, which renders 1/T(n)^2 as limited by 0 for positive curvature k=1.

So the k=1 ellipsoidal curvature in 11D is equivalent to the k=0 curvature of the asymptotic 10D universe by definition of 8 via 2* and 2 and 1.

The hyperbolic curvature k=-1 for openness is simply the imaged complex solution for the k=1 scenario mirroring 10D-Omnispace in 12D-Omnispace.

One can see this in the half-scale and the definition process for the beforementioned cosmic wavefunction describing the cosmic wavefunction {B(n)=(2e/hA).exp[-Alpha.T(n)]} which is the n=-1/2 Functional-Riemann-Bound (FRB) of the Riemann-Hypothesis in pure number theory.

To analyse B(n) (from the differential equation dB(n)/dT(n)+Alpha.B(n)=0), one uses the mirror property of OmniSpace in solving T(n)=1 and T(n)=-1.

T(n)=1 yields our Fibonacci Roots X and Y and the Euler Identity: XY=X+Y=-1=i^2=exp(i).

But T(n)=-1 changes the sign of the constant in the generating quadratic n^2+n (+/-)1=0; which is just the curvature k in General Relativity.

The solution for T(n)=-1 as n^2+n+1=0 changes the exponential term in the B(n) to its inverse in modular duality and gives complex roots about the FRB as -1/2(+/-) iSqrt(3).

Now assume a 'doubling' of {} in (2**) to reattain the Schwarzschild solution from the 'de Broglie' inflationary preepoch of the superbranes.

Then {1/T(n)^2+k}=2, which for k=0 and the asymptote requires T(n)^2=1/2, namely the reflected FRB from the B(n) and the Riemann Hypothesis.

Alternatively, we can consider T(n)=1=k for n=X, again combining the curvatures for the asymptotic approach and the higher dimensional encompassment.

A finestructure for this curvature unity is our (R(n)/Rmax)*(Rmax/R(n))=(n/(n+1))*(1+1/n)=1 in the

modular duality which is prevalent in the pentagonal symmetry of omnispace.

Expressing a fractional curvature then finestructures k in say 2=1+k(1+Y) with k=1/(1+Y)=1/(X+2)=X^2.

(Actually the pentagonal symmetry in omnispace derives precisely the (X+2) mapping for the gravitational interaction to unify the symmetry broken in the four fundamental force interactions with invariant X mapping Alpha as the Electromagnetic Interaction and (X+2)=1/X^2 mapping X^3 in the Unification Polynomial U()=^4+2^3-^2-2+1=0 or [1-][][+1][+2]=1 as the G-Alpha=Alpha^18.)

The Standard Deviation for normalised B(n) is 1/Sqrt(2Alpha) and so the variance converges to n^2=1/2 with mean the FRB (say in Chi^2 Probability-Density-Distribution of the central limit theorem, which says that a normal distribution of means results for normally distributed individual means).

R(n) can also be written as R(n)=Rmax - ct/T(n) for T(n)=ct/(Rmax - R(n)).

The Radius of Curvature of a sphere say is the Radius R with its reciprocal 1/R the Radius of Curvature for the Surface.

This is just the applied premise of modular duality which is more elementary in allowing operational definitions for this inversion (in Fourier transforms of displacement and momentum vectors).

But if Rmax is the Hubble Radius for a 4D-Volume as a 3D-Surface, then 1/Rmax is the curvature of the

3D-Volume as a 2D-Surface that is Poincare's 3-Sphere as Riemann's Hypersphere.

Geometrically, the convergence of the squared standard distribution or variance to n^2=1/2 is the intersection of the curvatures in R(n)=Rmax(1-n/(n+1)) and the curvature function C(n)=Rmax/(2n+1).

n/(n+1)=1/(2n+1) gives 2n+1=1+1/n for 2n^2=1.

But the derivative of T(n) is T'(n)=dT(n)/dn=2n+1 which as stationary value is 0 for n=-1/2, that is the FRB.

So C(n)=Rmax/T'(n)=R(n)(1+1/n)/T'(n).

Recall that the derivative of the Logarithmic Functions are Inverse Functions, say if y=ln(x), then dy/dx=1/x and so integrating the inverse functions as the curvatures results in logarithmic functions or their expanded infinite series. This relates of course to the fact that if y=e^x, then its derivative and integal remains as itself in dy/dx=e^x.

The important generalisation is that the ratio f'(x)/f(x) integrates to ln(f(x)).

For example integrating 2x/x^2=2/x gives ln(x^2)=2ln(x) and integrating tan(x)=sin(x)/cos(x) gives -ln(cosx).

Another interesting aside in "" follows to show the intrinsic nature of the parameters in regards to the quantum physics which demetricate General Relativity.

Let T(n)=1 map Rmax^2-R(n)^2=a^2-b^2=(a+b)(a-b)=T(n)=(n+1/2)^2-1/4 for a=(n+1/2) and b=1/2.

Form the ratio (a+b)/(a-b)=1+1/n as the definition basis for exponential and logarithmic functions.

a/b=2n+1 as T'(n) and so a/b=Rmax/R(n) reflects Radius R(n) in Curvature 1/R(n) (in analogy of superstring EpsEss coupling via constant h^2 (Planck's Constant squared) in partition Eps*Ess).

So for T(n)=1, T(n)=constant K^2=Rmax^2{1-n^2/(n+1)^2}=(2n+1).Rmax^2/(n+1)^2=(nRmax)^2.L, where constant L=T'(n)T(n)^2.

Convergence is established by: L=[1/n^2 - 1/(n+1)^2] in the limit (n->Infinity){1/1-1/4+1/4-...-1/(n+1)^2}=1.

Then 1=K^2=L(nRmax)^2=(nRmax)^2*(1/n^2 -1/(n+1)^2).

But we already know that nRmax describes the expansion of the 11D universe into 12D F-space and that L represents the Rydberg Finestructure for the Bohr Atom.

{An electron of mass me and (de Broglie wavelength) e is defined in mec^2=hf=hc/e and for an electron to be absorbed or emitted in light matter interaction, its wavelength must be proportional to the electromagnetic finestructure constant Alpha in the Compton wavelength Compton=Re/Alpha via 1/e=T(n)*mec^2/hc=T(n).Alpha.mec/(60e^2) for proportionality constant T(n) and h=60e^2/Alpha (from superbrane parameters and e the electron charge quantum).

But Re, the classical electron radius defining the quantum scale for all particles as the superstring quantisation of ps in Re=10^10*ps/360 can also be written in terms of the electron mass as Re=30e^2/mec, which sets 1/e=T(n).Alpha/2.Re.='Constant'{1/n^2 - 1/(n+1)^2}.

The atomic quantisation number Z^2=2n^2 as the variance n^2=1/2 and the Rydberg Constant (at infinity) is Ry=Alpha^3/(4Re) as 'Constant'=Z^2.Ry for finestructure T(n)=1=K^2, with (nRmax)^2 mapping (Alpha.Z)^2 /2 in the variance definition for Alpha as Alpha= ^2(1/2)/(2.Variance).

The first eigenstate (n=1) for the hydrogen atom becomes 1/n=-Alpha^3.Z^2./4Re with Rydberg Energy Ryhc=13.856 eV and first Bohr Radius RB1=2h^2o^2.e*/e^4=5.217x10^-11 metres, where e* is the primordial magnetocharge defining superstring energy Eps=1/e*=ps.fps"".

tbc and to be forwarded (the below is subsequent data yet to be fully exposited)




It is then evident, that the demetrication of the General Relativity parameters in dimensionless cycletime n not ony defines the expansion parameter a, but also redefines the Hubble Law in its boundary conditions.

We now understand how the 10D-Universe expands asymptotically under the demetricated form for Einstein's Curvature Radius R_C=c.dt/dn, with n a dimensionless cycletime defined in the nodal Hubble-Constant H_o=dn/dt as the Universe's Self-Frequency for the Hubble-Oscillation in 11D-M-Space.

The demetricated Velocity-Differential is v(n)=c/[n+1]² and the demetricated Deceleration-Differential becomes a(n)=-2cH_o/[n+1]³ (Milgröm Parameter and defining the asymptotic deceleration as the overall deceleration of C-Space modified by a Gravitational Omega and a Quintessential Lambda).
The Omega and the Milgröm Parameter are always negative, whilst the Lambda evolves from an antigravitational de Broglie phase state, to reach its asymptotic gravitational vanishing value after three zero states defined by the Temperature/cosmological redshift evolution of the cosmos (the first root being at redshift 2.15).
The so called 'cosmological constant' in Einstein's Field equations is thus the Intrinsic Milgröm Acceleration differential between the Omega and the Milgröm Parameter.

But the 'Volume' for the 10D-C-Space grows in the factor 2π²R³(n), whilst the 11D-M-Space grows in the factor n.2π².R_max³ for a DIM-Factor of V_11D/V_10D=[n+1]³/n².

This calculates for the present epoch as DIM=7.56.. and describes the 'missing' mass or dark matter.

The baryonic inertial mass-seedling of the deceleration parameter of 2.81% of the critical mass-seedling and has 'evolved' to about 3.68% in a coupling to the gravitational constant evolution from its 'massless-permittivity' initialisation of G_o.

DIM(3.68%)=27.82% and represents the Total Manifested Universal Mass in 11-dimensional M-Space.

Hence no 'dark matter' scenarios are necessary and the Milgröm Parameter suffices to account for the galactic rotation curves, seemingly violating Newtonian Gravitation in the necessity for 'dark matter haloes' of gravitating but nonluminous mass distributions.

We recall, that the critical mass-seedling (of about 6.4x10⁵² kg) gives the Euclidean flat curvature superimposed onto the hyperbolic 10D-Space of diminished mass content in restmass-seedling M_o (of about 1.81x10⁵¹ kg, now 2.38x10⁵¹ kg).

The Creation of spacetime quanta occurs in the 11D-M-Space not reflected back into the lower dimensional 10D-C-Space as the OmniSpace Mapping of the LineSpace described previously.

We have already calculated that X=Z.H_o~1.9x10¹²⁹ spacetime quanta are added every second to the Outer Boundary of the Universe as the refracted part of the Hubble-Oscillation.

An infinitely expanding hypersphere would however violate the Holographic Bound set in Black Hole parameters for the Information Content described by the Black Hole's Surface Area, quantised in Planck-Areas.

Yet, we also know that the Black Hole Event Horizon is LIMITED by the M-Space as the asymptotic boundary for the C-Space to 'expand into'.

This is of course QR's HB-Bound Z~10¹⁴⁷ Bits which itself sets the parameters for the continuous creation of the spacetime quanta.

The resolution and consequence henceforth is the modular duality and interconnectedness of OmniSpace.
The 'growth' of the 11-dimensional form of the Hypersphere continues unimpeded with the boundary conditions for the HB satisfied in its 10-dimensional Hologram of the C-Space, always bounded in the Steady State of the Hubble-Oscillation.

However what is defined as the 10D-Hypersphere is developing new degrees of freedom based on the multidimensional proprtires of translational LineSpace, Rotational HyperSpace, Vibrational QuantumSpace and Quantisational OmniSpace.

This results in the major axis invariance of the prolate ellipsoid describing the encompassed hypersphere to engage in phaseshifts to define the Multiverse from the Protoversal Universe.

A prolate ellipsoid becomes an oblate ellipsoid under minor axis rotation, as the previously fixed focus points of the ellipticalcross-section are forced to move as the locus of a point-circle.

The angular displacements for the minor axis rotating Protoverse, then define an infinite number of Potential Universes with a minimum of two such phaseshifts defining a Multiverse.

The sumtotal of all possible phaseshifted Multiverses, then constitutes the Omniverse; as the refraction part of the 11-dimensional Hypersphere adding Information at the rate of the QR HB in Z.

Thus all boundary conditions are satisfied within the Omniverse as the evolved Universe; understood and constructed by the sentience responsible for the cosmogenesis herein described in co-creativity.
The great fallacy in the standard cosmology in regards to the expansion of the universe is the assumption of a 'continuing stretching of the basic spacetime metric'.
The Euclidean universe of observation and measurement is flat and of zero curvature; because there was just the one 'stretching' of space in the  inflation of the de Broglie hyper acceleration, often termed the inflaton-instanton of timeinstantenuity.
There exists so no ever-receding Hubble-Horizon, with particular galaxies receding 'out of view' and similar consequences of a continuing 'stretching of the basic metric'.