A remarkable finding of the early 21st century, that kind of sits alongside the Nobel prize winning discovery of the universe’s accelerating expansion, is the finding that the universe is geometrically flat. This is a remarkable and unexpected feature of a universe that is expanding – let alone one that is expanding at an accelerated rate – and like the accelerating expansion, it is a key feature of our current standard model of the universe.

It may be that the flatness is just a consequence of the accelerating expansion – but to date this cannot be stated conclusively.

As usual, it’s all about Einstein. The Einstein field equations enable the geometry of the universe to be modelled – and a great variety of different solutions have been developed by different cosmology theorists. Some key solutions are the Friedmann equations, which calculate the shape and likely destiny of the universe, with three possible scenarios:

• closed universe – with a contents so dense that the universe’s space-time geometry is drawn in upon itself in a hyper-spherical shape. Ultimately such a universe would be expected to collapse in on itself in a big crunch.

• open universe – without sufficient density to draw in space-time, producing an outflung hyperbolic geometry – commonly called a saddle-shape – with a destiny to expand forever.

• flat universe – with a ‘just right’ density – although an unclear destiny.

The Friedmann equations were used in twentieth century cosmology to try and determine the ultimate fate of our universe, with few people thinking that the flat scenario would be a likely finding – since a universe might be expected to only stay flat for a short period, before shifting to an open (or closed) state because its expansion (or contraction) would alter the density of its contents.

Matter density was assumed to be key to geometry – and estimates of the matter density of our universe came to around 0.2 atoms per cubic metre, while the relevant part of the Friedmann equations calculated that the critical density required to keep our universe flat would be 5 atoms per cubic metre. Since we could only find 4% of the required critical density, this suggested that we probably lived in an open universe – but then we started coming up with ways to measure the universe’s geometry directly.

There’s a You-Tube of Lawrence Krauss (of Physics of Star Trek fame) explaining how this is done with cosmic microwave background data (from WMAP and earlier experiments) – where the CMB mapped on the sky represents one side of a triangle with you at its opposite apex looking out along its two other sides. The angles of the triangle can then be measured, which will add up to 180 degrees in a flat (Euclidean) universe, more than 180 in a closed universe and less than 180 in an open universe.

These findings, indicating that the universe was remarkably flat, came at the turn of the century around the same time that the 1998 accelerated expansion finding was announced.

So really, it is the universe’s flatness and the estimate that there is only 4% (0.2 atoms per metre) of the matter density required to keep it flat that drives us to call on dark stuff to explain the universe. Indeed we can’t easily call on just matter, light or dark, to account for how our universe sustains its critical density in the face of expansion, let alone accelerated expansion – since whatever it is appears out of nowhere. So, we appeal to dark energy to make up the deficit – without having a clue what it is.

Given how little relevance conventional matter appears to have in our universe’s geometry, one might question the continuing relevance of the Friedmann equations in modern cosmology. There is more recent interest in the De Sitter universe, another Einstein field equation solution which models a universe with no matter content – its expansion and evolution being entirely the result of the cosmological constant.

De Sitter universes, at least on paper, can be made to expand with accelerating expansion and remain spatially flat – much like our universe. From this, it is tempting to suggest that universes naturally stay flat while they undergo accelerated expansion – because that’s what universes do, their contents having little direct influence on their long-term evolution or their large-scale geometry.

But who knows really – we are both literally and metaphorically working in the dark on this.

**Explore further:**
Dark statistics

## remoran

## rawa1

http://www.prophe...niverse/

and/or the space gets lower or higher dimensionality with distance

http://atramateri...niverse/

http://www.nasa.g...023.html

For every article like this one I can cite another article, which is claiming exactly the opposite. In another words, you can write what you want about Universe today - which is definitely not good with respect to public belief in mainstream cosmology.

## rawa1

http://www.aether...ples.jpg

The situation can be even complicated with fact, even the water surface is never completely flat, so we would observe the space-time deformation even if we would observe it from steady-state perspective (compare the Doppler anisotropy of CMBR or fine structure constant, dark flow, parity violation and another findings observed recently at the cosmic scale).

## Shootist

## rawa1

The similar situation occurred before four hundreds of years, when Galileo and others started to promote the extrinsic perspective of solar system. Whereas the existing models were based on epicycle perspective of planetary motion, i.e. the perspective of human observer, who is sitting on the Earth and who is observing the solar system from inside.

The point is, the extrinsic perspective is more difficult to prove (believe it or not, we still never observed the planetary motion of Solar system from outside) - but it simplifies and reconciles the existing rigorous models, which are based on intrinsic perspective.

The experts are never happy from such turnaround, because they must learn new paradigms and they're facing the lost of jobs connected with reduction of old theories.

## Eoprime

## rawa1

http://people.rit...4565.jpg

Under such a situation we are observing the observable part of Universe both from intrinsic, both from extrinsic perspective at the same moment and both approaches will converge mutually. In dense aether model the event horizon of black holes represents the fragments of outer surface of Universe, as being observed from inside it from perspective of distant past. And the surface of elementary particles represents its inner surface, as being observed from perspective of distant future of Universe.

## Erscheinung

## rawa1

Try to imagine the shinning light bulb in the deep bucket covered with pile of foam. Whole volume of foam will glow - not just interior of bucket. Which means, we can observe the bucket both from outside, both from inside of it, because the light of bulb is heavily dispersed into all directions possible. You can remember the Möbius strip and/or Klein bottle geometry in this connection.

## thales

That's an interesting idea. Light doesn't contract space-time, but I think I see what you're trying to say. The speed of light is really a measure of a space-time boundary, and there may be a connection between that measure of space-time and its flatness. Or something.

## hush1

Poincare's Conjecture:

All shapes and forms without a hole is a sphere.

When you realize what this means for all Geometry, you will find Euclid insufficient, unnecessary, and incomplete.

The new paradigm is:

All Geometry is Poincarian, not Euclidean. And when one does this, n-body problems are no longer intractable. Field equations have exact solutions, and protein folding problem is solved.

## Pyle

## typicalguy

## hush1

lol guy. A disciple-ian collarory of raw1's interpretation. Do you have his approval?

## hush1

## hush1

A book?!?! You want a book of conjecture?

It's too late to use Poincare's Conjecture.

Using proven conjecture to conjecture is silly.

## hush1

## hush1

A subliminal and superluminal typo.

## Erscheinung

## Erscheinung

I tried and tried but couldn't get any clarity here,...

http://www.physor...ong.html

His arrogance in the above thread is comical especially sense one can't pry out any semblance of the idea.

(Noumenon)

## hush1

I can not provide reference where the solution to the Poincaré conjecture has allowed cosmologists to determine anything meaningful about the large scale structure of the universe.

Is this connected to both of your questions?

## Isaacsname

## Erscheinung

Ok then, can you elaborate any on the meaning of the above? GR already uses a non-Euclidean geometry. What's the difference between "Poincarian" and Riemannian?

## hush1

"Sometimes an otherwise complicated operation reduces to multiplication by a scalar (a number). Such numbers are called eigenvalues of that operation. Eigenvalues are closely related to vibration frequencies and are used in analyzing a famous problem: can you hear the shape of a drum?. Essentially an eigenvalue is like a note being played by the manifold. Perelman proved this note goes up as the manifold is deformed by the Ricci flow. This helped him eliminate some of the more troublesome singularities that had concerned Hamilton, particularly the cigar soliton solution, which looked like a strand sticking out of a manifold with nothing on the other side. In essence Perelman showed that all the strands that form can be cut and capped and none stick out on one side only."

http://en.wikiped...njecture

## hush1

The curvature derive for non euclidian geometries come from the Euclidean.

Only 'flat' is not 'flat' even for euclidean geometries.

The definitions for euclidean geometries are superseded by Poincaré conjecture.

Even though the definitions define 'flat' for euclidean geometries, there is still 'curvature' there.

The quote is merely to show the practicality and connections to the physical - Can you hear the shape of a drum - sounds 'tangible' to anyone.

## hush1

## hush1

My name is Hush. That's how people address me when they do not want to hear...any shape.

## Erscheinung

http://sofia.nmsu...care.pdf

Is this what you mean?

## hush1

Figuratively, the "Poincarian" puts in or takes up the 'slack' the Riemannian ignores or introduces.

## primalvisions

Anyone have a link to more of his lecture?

## ArmyFighter04

## Pyle

Dark Matter and Dark Energy are plugs, placeholders, unknown things that are observed, but as of yet unexplained and not yet completely understood.

The DM amount in the early universe is what is required to make the BB work using the theories we have now. Theories that have been supported time and time again by our most accurate measurements of experiments and observations of the universe.

The DM amount currently is more of the same; what is necessary for the universe to work if our current standard model is correct. The DE similarly to explain our observations (flatness/red-shift). DE may have been there all along, not doing anything, and only recently has been "turned-on" and is influencing the Universe. Or maybe it is all wrong and something else is going on at the grandest scale.

In any event, don't math your way between the two charts, that isn't what they are meant to be used for.

## Seeker2

DE may have been there all along, not doing anything, and only recently has been "turned-on" and is influencing the Universe

That is, compress a spring (or spacetime if you imagine it to be compressibile - it certainly is expandable). There's lots of energy there but you never know it until you release the compression. So - DE may be there and have been there all along in the form of some potential energy beginning to be released at the big bang.

So what happens when the compression energy is all used up (assuming it is finite) - does spacetime (the springs) continue to fly apart? Yes, maybe, but the acceleration stops. But what happens if the springs hang together and begin to be stretched? It could be deja vu all over again.

## Cynical1

## omatranter

"we are both literally and metaphorically working in the dark on this."

Being "7th Dan Black Beat" in the art of self satisfaction I can assure you that making your hand go to sleep as well it heightens the pleasure of "The Stranger"

(http://www.urband...ranger), I also find the excited utterance "Replant Neutrons Assemble" makes my day.

## cps

Perhaps what's really happening is something like Mach's principle. Matter near the centre of a galaxy sees lots of matter around it so experiences a large centrifugal force whereas on the outskirts of the galaxy (or in dwarf galaxies) there's less matter to constrain the rotation.

## Seeker2

I thought centrifugal force comes from rotation? Maybe objects aroung the center affect its rotation? Interesting.

## vidyunmaya

sun is not flat with Earth Planet ?

Even the Milky defies your Flat-Universe Logic ?

Cosmology needs best of Best of brains Trust- Scientists have Credibibility at stake ?How do we stand-up with Conscious Head! Cosmology Vedas Interlinks help in time. Vidyardhi Nanduri

## vidyunmaya

Cosmology Studies-Science to Progress

Cosmology needs best of brains trust.Understanging Nature and Philosophy is a long way for Comprehension. Basic functions-Source,Fields,Flows,Reflectors are ignored-Leave alone protective functional Index. From and above these Concepts, One needs to define Cosmology and identify Prime concepts.

See: BOOKS BY VIDYARDHI NANDURI [1993-2011]-

http://vidyardhic...pot.com/

## DarkHorse66

;) So..what's YOUR shape? Or, at least, how do you perceive it to be? It's rather hard to infer the nature of something, when it is absent (or perceives itself to be thus). But then again, silence is supposed to be golden.....synesthesic connection perhaps? Hehe DH66

## hush1

lol DH

Out of shape right now.

Out of shape shapes sound strange.

When heard.

## jinsincity

## jinsincity

## jinsincity

## jinsincity

## Pirouette

## Daleg

but there is plenty of room for wider speculation about why we live in a flat Universe when most Astronomers based on observations would expect we live in an open Universe, but as the old saying goes, you have to take it as you find it, all pet theories aside.

## Daleg

It is taking Gravity as negative or purely attractive into account in Einstein's Theory which indicates the paradoxial effect that the energy content of the Universe may be zero. Einstein's theory isn't wrong, the statement that the Energy content of the Universe =0 is an explanatory guess as to why space is flat, as measured, and an attempt to remove all curvature by making the energy content =0, through the negative contributions of Gravity, could just possibly be the right answer.

## Daleg

and demonstrates. The reference to "correcting" the Reimanian meric tensor, means just that making sure it does and can maintain the "correct" curvature through constant change in scale over time, otherwise you create anamolies which destroy the ability to measure the resultant curve and cannot prove the theorom of the contraction of a sphere in all three dimensions down to a single point.

## Daleg

## bluehigh

I thought with a US accent it would be more like 'rah-jar'. Here, its more like 'roh-ja'. In any case a worthwhile distraction.

## hush1

First the earth, and now the universe is flat!! lol. The only form of life in the universe existing and living on a curve!, manages a construct labeled 'line' and 'flat' first, for starters, and the curve second!!! lol

And then to conjecture what is to be incomprehensible for flatlanders!!! lol

And then wonder why angles can't be trisected, and the quadratures of circles offering nothing but frustration!!lol

Imagine the curve being first. Imagine all the hyperboloid buildings and architecture of the ancients. Imagine humans trying to revert and revamp their dwellings to conform to a 'line', or 'flat' or god forbid a box!!

Unimaginable. No human can be that stupid.

Thanks Euclid. Way da go. You have no idea what you done.

Our celestial mechanics are screwed, GR embeds you locally, QM is utterly clueless and we can't fold proteins. Whatever.

## nickelsworth

I've no equations ,theorems nor empirical truths. That said, I do know wave patterns and propagation. It seems the forest cannot be seen through all the trees. Stabilization is Chaos; as much as Chaos is Stabilization. It may be better to first get a firm understanding of the nature of things in our own small woods called the solar system. The study of our own sun will answer more questions than the forests light years away. P.S. 'Pi to the 10 Trillionth Digit' = 5

## Callippo

The convergence of both approaches illustrates, your insight has some merit in context of dense aether model.

## Callippo

## Seeker2

Well Callippo maybe human thinking is driven by the uncertainty principle?

## Seeker2

...At the very general level the behavior of people can be approximated with energy spreading in dense gas,

I guess our reputation precedes us wherever I go. Sort of like Charlie Brown's friend Linus?

## Seeker2

...and maybe we are a closed universe.

Flat - by actual measurement, as in the de Sitter solution to GR. Riding on top of this basic solution are some minor(?) perturbations caused by the uncertainty principle - the creation of matter/antimatter. Dark matter I attribute to turbulence in the de Sitter spacetime expansion function caused by the uncertainty principle. You might look at it as de Sitter (spacetime) is the carrier frequency and matter and radiation are AM and FM modulation.

## Seeker2

In a previous life I used to sit in second-year French class with a frat bro who tempted me with his cigarettes. I obliged. We sat in the second row with our feet propped up on the front row seats and blew smoke rings up on the blackboard. Nobody really cared that much since we were the only two in the class. We got pretty good at it. I didn't realize at the time that I was simulating rings of high-density spacetime (dark matter) blown away by the BB and later forming galaxies. So the U is a happy hybrid of GR and QM. May the two live happily thereafter.

## Cynical1

The article stated that repeated observation of an element of a system, in fact predicted how that dynamic system acted.

So, inasmuch as we are ALL elements of any number of "systems", perhaps Calippo's on to something there... And Seeker, too...

## Seeker2

...there was an article that found a particle traveling 12 nanoseconds faster than the speed of light - ...in this article it clearly states that the universe = 0 total energy

Daleg:

...through the negative contributions of Gravity,

I think I heard this from Hawking but he was only talking about mass and gravitational potential energy. I would extend it to anti-matter and anti-gravitational potential energy (if you've been around much you've probably encountered my theory of anti-gravity).

## Seeker2

...Physics should also be able to predict when the outward force will stop and when the universe will begin its steady force over time of collapsing upon itself, its apex then its return correct given it is flat ?

I suppose expansion will stop when the dark energy is used up, assuming it is finite. So the dark energy is now 73% of the total. 27% was used up in 13.7 billion years, so I guess you can do the math for when it will stop expanding and start contracting and returning mass/energy to the dark energy. I'm assuming conservation of energy over time.

## hush1

I work with the hyperreals. If you can maintain the curvature flow over the hyperreals down to a limit - the point - the point must exhibit a Euler characteristic. Infinite density and temperature is perfect paired - not a problem.

I need a characteristic of zero in the field. Which excludes Euclid and retains curvature. A curvature as an absolute reference. This point has no volume, space, time, or length. It has infinite density, temperature and curvature.

## Seeker2

...if the universe is expanding, what is it expanding from ?

From the dark energy, I suppose, concentrated in a very small (maybe Plank) volume.

...what is "outside" the conical shape?

The void, I suppose, if anything. Others I guess say the vacuum.

...this would make it likely that there could be many "universe" situations

Yes, some say an infinite number of situations - everywhere throughout all time and before if there is such a thing, but I don't work with the hyperreals.

...that all started with a infinitely dense and infinitely small particle

That seems to imply a zero volume. The uncertainty principle would rule that out.

## Seeker2

...At the very general level the behavior of people can be approximated with energy spreading in dense gas,

Another reference to Linus? Sorry.

## hush1

Assigning properties to 'nothing' is as common as the weather.

Zero, the workhorse. Another workhorse: Infinity.

Harnessing the two horses pulls any carriage.

This is poetical. Without 'pulling a fast one'. Why?

To free all readers imaginations daunted by horses.

## hush1

Beyond that point you declare:

Nothing is physical.

Nothing has meaning.

Math is devoted to that which has no meaning and is never physical.

Not once has science failed to find meaning to the imagination of math.

All else is failure of imagination.

## Callippo

In recent time various thermodynamical models of human evolution became popular. What do you think the thermodynamics is all about?

http://www.physor...868.html

http://www.physor...278.html

Isn't it a bit sad, when the people, who are visiting physorg regularly cannot even remember the articles presented just here? You people are of zero memory, not to say about ability to combine the existing knowledge. Instead of it, your ability to downvote everything, which you're not familiar with is extremely well developed.

As the result, the people who can remember and combine stuffs are systematically oppressed with people, who cannot do it. The trolls always win with their very nature.