Shape of Universe: Is Flatness Approved? Causes of Big Crunch

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The universe is currently considered to be flat with a 0.4% uncertainty, primarily supported by data from the WMAP and other observational studies. While the LCDM model, which is widely accepted among cosmologists, does not predict a big crunch, there is ongoing debate about the universe's curvature, with some recent findings suggesting a slight positive curvature. This means that while the universe is nearly flat, it could still be part of a much larger closed structure. The acceleration of the universe's expansion, attributed to the cosmological constant, indicates that a big crunch is unlikely, leading to predictions of a "big whimper" instead. Overall, the shape of the universe remains a topic of active research, with future data expected to refine our understanding.
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How certainly is the universe flat? Is is absolutely approved or not?
If yes, what will cause the big crunch?
 
Space news on Phys.org
Thanks to WMap our certainty of the shape of the universe is considered flat with an uncertainty of 0.4 % . However as the vacuum energy density is greater than the critical density we are expanding and not predicted for a big crunch. Unless something unpredicted were to happen. Rather were destined for the big whimper.
The Thread " Look 88 B Years into the future and see the Universe shaping up " posted in the sticky threads above has some powerful tools in the calculators. In the sticky thread on the balloon analogy their is also some good articles covering expansion.
 
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Chemist@ said:
How certainly is the universe flat? Is is absolutely approved or not?
If yes, what will cause the big crunch?

There are various non-standard models in which the constants vary and different things happen, but the standard consensus model that most cosmologists use and fit the data to, as new observations are made, is the LCDM model. This has no big crunch.

The overall mean curvature for the LCDM has been measured over the years and the error bar for it has been gradually shrinking down as more and more observational data is acquired.

I forget the actual latest figures on the curvature---basically, very roughly, it is something like with 95% certainty we think it is zero plus or minus 1%. that is, we do not know that the U is spatially flat, but we are fairly sure that it is very close to flat.

As I recall a very recent report, from South Pole Telescope, said that with 95% certainty the curvature was not zero but just a wee bit on the positive side of zero! So that while the U is not infinite (according to them) it is so nearly flat that the hypersphere circumference could be as large as 880 billion lightyears. That is, the 3D analog of a sphere so that if you could stop expansion right now and sail off at light speed in some direction you could travel in a straight line for 880 billion years before you found yourself back home. But it might not be that near flat, or that large--there is a range of uncertainty about the mean curvature.

This finiteness (if it is a fact) does not imply a crunch because we have learned about the acceleration resulting from the small measured value of the cosmological constant Lambda.

LCDM stands for Lambda cold dark matter.
 
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So far, a flat or near flat ever expanding universe seems like a very good bet.
Yet we have been fooled many times thru the ages:

The Earth was NOT the center of the universe,

and up through about the 1920's...

We thought the universe was our own Milky way galaxy,
we thought the universe was static...up through the 1920's,
we thought we knew about 99.9% of the matter in the universe...then up popped 'dark matter'
 
In the thread I mentioned above Marcus is one of the best qualified to explain how to use it.
 
Thanks to everyone for their replies.

Even as a child I was thinking about the shape of the universe and I thought that it probably won't be determined in my lifetime. Now, I feel really satisfied. In a great time we live.
I got few more questions if it's not a problem:

1. When was the shape of the universe approved with the 0.4% uncertainty?
2. Below is a picture of the flat universe:
http://img607.imageshack.us/img607/412/55426705.gif
The arrow is pointing towards the smallest dimension of the universe. How wide would it be? It shouldn't be that long (relatively speaking).
3. Marcus, did you mean in your post that if you reach one end of the universe from your home, you will start at the another end and that way you can return home?
 
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I detect your under a few misconceptions of the answers provided.
1) a flat universe does not imply closed or open both possibilties in a flat model.
The strongest data for the shape og the universe was released with WPAPS 7 year survey of thr CMB. I have the findings of WMAP though heavily on technical detail. Many of the posters on this thread have the same.
Marcus post is in reference to South post findings in favor of a closed universe.

Remember that flat does not imply closed or open. Open is infinite in size. The post by Marcus describes possibility of closed but REALLY huge.
 
From which year are these data?

How would a flat closed universe look like?
 
Chemist@ said:
T


1. When was the shape of the universe approved with the 0.4% uncertainty?

The resulting shape is 3d 'flat' euclidean w/ .4% uncertainty based from data collected using several methods like subgrading type (large-scale nonsmooth convex). Picking each saddle points of convex-concave in the area of the map; solving its variational inequalities and some techniques for unconstrained minimization of smooth convex functions (Gradient Descent,
Conjugate Gradients, quasi-Newton methods with restricted memory, etc.). There is a .4% margin of uncertainty where it is impossible to exactly describe the existing state.

The report was submitted 20 Dec 2012, last revised 30 Jan 2013.
http://arxiv.org/abs/1212.5226

Here you can play on the values of CMB...

http://map.gsfc.nasa.gov/resources/camb_tool/cmb_plot.swf
 
  • #10
Okay, thanks. I need answers to 2 and 3. What is the most approved shape, open or closed?
 
  • #11
marcus said:
As I recall a very recent report, from South Pole Telescope, said that with 95% certainty the curvature was not zero but just a wee bit on the positive side of zero!
Yeah, but I wouldn't put any stock in that. Not yet, anyway. That's just not significant enough to say anything.
 
  • #12
Chemist: try reading here for some background and alternatives...

http://en.wikipedia.org/wiki/Shape_of_the_Universe

Open versus closed is unknown, but maybe if a vote was taken one or the other would be more popular??

Shape: who knows?? A three space dimensional Mobius strip would be especially fun. Then China would not just be upside down but 'inside out'...[note to police: just a JOKE!]
 
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  • #13
Chemist@ said:
Okay, thanks. I need answers to 2 and 3. What is the most approved shape, open or closed?

If you mean "accepted prior to current/accumulation of data's". It is humongous-ly flat but then again we do have slight positive curvature which give you the impression that it might be huge/closed. Until we have a definitive constraint to what a 'UNI'verse should be. Open or closed remains open to criticism (consequence of that small curve). Till then we rely on mathematical predictions and hope data's fit directly to it. To answer your question. In general. It is 'uncertain' unless you put a probabilistic value to it.
 
  • #14
The human mind is a funny thing, . It tends to fill in the missing blanks with whatever it desires and then we as sentient beings believe they are true reality and truly there even when they are not, This has been proven in many ways, (the optical illusion, the minds filling in of your optical blind spot in eye sight, filling in personal prejudices, etc), as for survival, our brain lies to us so we may predict and function in life, but we still believe what we see is real . .we also live on limited senses O(only five and each having its limits as well), and limited cognitive ability, . we as inferior mankind through our limited perception of the world, marvel at the impossibility of ideas like "entanglement", the "sole beginning bang of infinite time from nothingness" and even the the philosophical contradiction of the theoretical existence of "totally empty space" . .. like A rat, for example, may learn to navigate a maze that requires it to turn left at every second fork but not one that requires it to turn left at every fork corresponding to a prime number, . we must remember our own mental capacity is also extremely limited in the face of the expanse of the universe, . .. . perhaps in the distant future, after all our scientific experimentation is done, we as humans may find that the universe really, . . does not have any shape at all, . .
 
  • #15
If the universe is e.g. in the shape of the coat of a cylinder, what would be inside the cylinder?

Found on wikkipedia: The latest research shows that even the most powerful future experiments (like SKA, Planck..) will not be able to distinguish between flat, open and closed universe if the true value of cosmological curvature parameter is smaller than 10^−4. If the true value of the cosmological curvature parameter is larger than 10^−3 we will be able to distinguish between these three models even now.

Someone knows the latest info? How much is the cosmological curvature parameter?
 
  • #16
Chemist@ said:
Someone knows the latest info? How much is the cosmological curvature parameter?
We haven't yet definitively detected any deviation from zero. Could be 10^-3, 10^-4, 10^-10, 10^-100.
 
  • #17
Chemist@ said:
...
Someone knows the latest info? How much is the cosmological curvature parameter?

It's something to watch evolve as information comes in. The next installment will be delivered in just one month from now at a symposium in Holland.
http://congrexprojects.com/13a11/programme
On 2-5 April, the European Space Agency (ESA) is having its first meeting on the results from the Planck mission.

Skydive Phil noted that there is also a press conference scheduled for 21 March.

What WMAP did, with each new release of data, was to roll their data up with other studies to give a combined estimate based on all the available observation (appropriately weighted).
So WMAP would give its own 95% confidence interval, and also it would give the same thing for WMAP+BAO+SPT+SNe... (i.e. including South Pole Telescope and Supernovae studies etc...)

So when Planck mission reports a month from now they will probably give their own separate estimates of basic cosmological parameters and also probably give some estimates labeled Planck+WMAP+otherCMB+BAO+... or something like that.

The talk that cosmologists will be waiting for is at 2PM on the first day:
Session 2 (Plenary): Main Cosmology results
14:00 Cosmological parameters from Planck and other experiments
G. Efstathiou
=========================

So whatever numbers anybody digs up for you on the curvature right now are likely to soon be made obsolete by numbers from Planck combined with "other experiments", as per Efstatiou's talk. That said, I will get some recent numbers nevertheless.

https://www.physicsforums.com/showthread.php?p=4279205#post4279205
 
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  • #18
Okay, so all in all, the observable universe is flat with a very very slight deviation that we aren't sure of. On a larger scale (looking far beyond observable universe), if this deviation is high enough, then the universe would be cylinder shaped. If the deviation is small, the universe is open. Either way, the universe will have one dimension much smaller than the others. Are there any estimations of its length (of the smallest dimension)? Did I write everything correct?
 
  • #19
Chemist@ said:
if this deviation is high enough, then the universe would be cylinder shaped.
A cylinder is geometrically flat (you can bend a piece of paper into a cylinder without tearing).

If there is a slight positive curvature, then it's like our observable universe is a small piece of a very large sphere. If there's a slight negative curvature, then it's like our observable universe is a small piece of a large saddle-shaped surface.
 
  • #20
Chem,what Chally says here is very instructive (even though he dismisses the possibility that the latest data could be telling us something.) We can estimate the CIRCUMFERENCE of the "very large sphere" he mentions--in that case. And imagine "circumnavigating" to get a concrete mental picture of the experience.

Chalnoth said:
...

If there is a slight positive curvature, then it's like our observable universe is a small piece of a very large sphere. ...

By cosmologists convention, a slight positive curvature corresponds to measuring a slight NEGATIVE value of a number called Ωk.

==from the October 2012 SPT report, page 14 equation (21)==
The tightest constraint on the mean curvature that we consider comes from combining the CMB, H0 , and BAO datasets:
Ωk =−0.0059±0.0040. (21)
==endquote==
http://arxiv.org/abs/1210.7231

You can see that the most negative of the 95% confidence interval is Ωk =−0.0099.

This corresponds to a universe where space is like the 3D analog of the 2D surface of a sphere. Circumnavigating corresponds to heading off at the speed of light in some direction and (assuming expansion could be halted for the duration of your trip) it would take 880 billion years.

The formula you use is divide 88 billion years by the square root of the number 0.0099.
That is like dividing 88 billion years by 0.1, so it comes to 880.
 
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  • #21
I am a little confused now.

The biggest probability is that the universe as a whole is a sphere or the coat of a sphere?
 
  • #22
Chemist@ said:
I am a little confused now.

The biggest probability is that the universe as a whole is a sphere or the coat of a sphere?

The 3D coat of a 4D ball.

So if expansion could be halted to allow this, you could head off straight in some direction and eventually find yourself returning (from the other direction) to your home base.
 
  • #23
You mean time by the 4th dimension?

The coat would have a very short dimension. What would happen if someone reaches the end of it?
 
  • #24
Chemist@ said:
You mean time by the 4th dimension?

The coat would have a very short dimension. What would happen if someone reaches the end of it?

The balloon analagy in the sticky threads above offers some decent descriptions to answer this.
However if your thinking that the sphere would have an inside or outside that isn't the case.
One of the easiest ways to avoid confusion though not accurate. Is to think of the inside as the past and the outside as the future.
This like I said isn' t accurate however its a useful metaphor to avoid the inside-outside confusions that the balloon analogy always leads up to.

Also keep in mind their is no clear consensus if the universe is open or closed. At this point we can only say that it is flat or extremely close to flat.
As mentioned in a month as Marcus mentioned. We will be getting further data.
The sticky thread on the balloon analogy also has tons of useful links. I highly recommend the ones leading to Ned Wrights tutorials. Particularly his FAQ article. Its one of the better articles for those relatively new to cosmology.
Some things to add on the open closed description. If the universe is closed/finite now then its always finite. Same applies to infinite/open.
 
  • #25
Chemist@ said:
You mean time by the 4th dimension?

The coat would have a very short dimension. What would happen if someone reaches the end of it?

As I understand it, what you call the "coat" of a ball is what I would call a sphere.
in our 3d world, the ball is the solid thing and the sphere is the hollow thing. It has zero thickness. It is a pure 2D surface.

A dimension is a direction you could point, or move in.
Or, in the case of a 2D world, it is the direction a 2D animal living in a zero-thickness purely 2D surface could point, or move in.

As I understand it there is no "very short dimension" because you and I cannot point our fingers in any direction which is the 'thickness" of our 3d space. There is no direction that we can move that we would "reach the end of."
 
  • #27
Chemist@ said:
I am a little confused now.

The biggest probability is that the universe as a whole is a sphere or the coat of a sphere?

... Kinda tricky to get by. Just imagine the coat without the usual hollow part since were talking of geometry mainly euclidean space in which every point on the geometry is determined by 3 coordinate(x,y,z) and NOT the standard geometric analogy of a ball in a certain space or beyond space/beyond observer.

Imagine space is 'everything'/shapeless/boundaryless/limitless (sake of mental image) and within it is a canvas of light, matter, cosmic stuff etc etc. We can determine such topography/shape/etc etc by studying the sprayed/scattered/movement of things along that canvas to a degree(current observed limitation/surface of last scattering). How it will 'play' within that 'shapeless' space etc etc. And they came up with majority of flat and a twitch of curve. For more technical details check Marcus and Modred links/signatures.
 
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  • #28
marcus said:
As I understand it, what you call the "coat" of a ball is what I would call a sphere.
in our 3d world, the ball is the solid thing and the sphere is the hollow thing. It has zero thickness. It is a pure 2D surface.

A dimension is a direction you could point, or move in.
Or, in the case of a 2D world, it is the direction a 2D animal living in a zero-thickness purely 2D surface could point, or move in.

As I understand it there is no "very short dimension" because you and I cannot point our fingers in any direction which is the 'thickness" of our 3d space. There is no direction that we can move that we would "reach the end of."

What is then a 3D sphere?
 
  • #29
Chemist@ said:
What is then a 3D sphere?

How you define stuff depends on where you are coming from. If you are coming from an undergraduate geometry class then you have a standard way of defining a spherical geometry of any dimension, 1-sphere (a ring), 2-sphere (surface of ordinary ball), 3-sphere, 4-sphere, 5-sphere...etc.

You define it in terms of sets, functions, coordinate systems. Maybe the simplest way is to think of the infinitely thin surface of a ball, and then imagine that the ball itself does not exist, only the surface.

And think of the EXPERIENCE of an infinitely thin amoeba-like animal living in the spherical surface, that has nothing within it and nothing outside it.

For that animal, straight lines are what we would call "great circles". Like the sea-routes and air-routes on a globe. They are the shortest distance between two points.. that is what straight means basically.

The math I'm talking about was worked out around 1850. Although it had been brewing since around 1820. So you could call it MODERN geometry, as contrasted with Greek-style. People tend to think with Greek-style geometry ideas until exposed to modern geometry in college.

Modern geometry is, I would say, experiential. It focuses on the experience from within the geometry. Not looking at shape from the outside, as with the eye of some ideal external being.

Experience shape and curvature from the inside.
By checking to see, for instance, what triangles add up to.

At astrophysical distances triangles, after all, do not add up to 180. What they add up to can change. It can depend on how big the triangle is. We have no right to expect the distance between two stationary observers will remain the same. And so on. Everybody knows this.
So why assume that we are living in an old fashion GREEK geometry?

And we do not assume that there is anything OUTSIDE our geometry. Because there is no evidence that there is anything outside. We experience shape from the inside, and we do not imagine an "outside" of space.What would that mean,anyway? An "outside", in some direction we can't point to, is a highly speculative and an unnecessary complication.
 
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  • #30
Chemist@ said:
What is then a 3D sphere?
Well, the problem is that it can't be visualized. But it perhaps helps to think of the definition of a two-dimensional spherical surface, the 2-sphere. The 2-sphere is, in three-dimensional space, a set of points that are all equidistant from some center. One could similarly construct a 3-sphere in four-dimensional space (note: four spatial dimensions here, we're not even considering time just now), where each point within the 3-dimensional volume would be equidistant from the center of the 3-sphere.

But then we're back to the above problem: this can't be visualized. How can every point in a 3-dimensional volume be the same distance from some other point? It's mathematically correct, but our minds can't handle it. So it's probably better to take a step back and instead of asking what it a 3-sphere looks like from the outside, what does a 2-sphere look like from the inside?

One of the interesting features of a 2-sphere is that you can't draw a regular grid on it for very far: try, and far enough away from where you started, the parallel lines that make up the grid will start to get closer together. So you either have to deal with the parallel lines getting closer, or periodically cut out a grid point as you move. this, for example, is what is done in California's San Joaquin valley, where there is a reasonably-regular grid of roads, but if you look at the grid closely, you notice that every once in a while, a road in the grid is removed. This is because of the curvature of the Earth.

Another effect, and one that is more commonly discussed, is that if you draw a triangle, its angles add up to larger than 180 degrees if you try to draw it on a 2-sphere. An extreme example would be to draw a huge triangle on the Earth, one with a vertex at the north pole, and the other two vertices at the equator, a quarter of the way around the Earth from one another. This is a triangle, but all of the edges of the triangle meet at right angles! The triangle's angles add up to not 180 degrees, but a whopping 270 degrees!

And then there's the fact that a spherical surface wraps around on itself: if you travel far enough in one direction, you end up back where you started. Now, as a matter of practical fact, this can never happen with our universe (it's expanding too quickly for you to get very far), but if it were the case that our universe were a 3-sphere, and if we could magically halt the expansion, then we could get back to our current location simply by traveling very, very far in anyone direction. There are other ways for a universe to wrap back on itself (it could be donut-shaped, for example, a shape that wraps back on itself but has no net curvature). But a spherical surface is one way.
 
  • #31
Continuing post #29:

...So a 3-sphere is simply a finite volume space, with no outside (no boundary), where we consistently experience a pattern we call curvature (e.g. of triangles adding up to more than 180) wherever we go. We experience the same small positive curvature at every point in space.

It could be a 3-sphere geometry we are living in! Carl Gauss in 1820 suspected it might be and tried to get a government grant to measure a very large triangle between mountain peaks in Germany. The larger the triangle, he knew, the larger the effect. So he wanted to measure a really large triangle which might therefore have a detectable excess over 180, if the angle measurement was extremely precise.

Now in 2013 we are measuring triangles, using spacecraft observatories which are big enough to maybe detect that excess, that slight positive curvature, which Gauss imagined. If it exists, or else if it doesn't then to find out there isn't any.
 
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  • #32
marcus said:
Now in 2013 we are measuring triangles,
I think you missed, "That stretch across the visible universe." :)

Anyway, I thought I'd just point out something. If you examine the paper you linked earlier:
http://arxiv.org/abs/1210.7231

...you'll note that the positive curvature result is peculiar to the combination of SPT, WMAP7, and BAO. If you don't include BAO, but do include a measurement of H_0, the result is nearly as tight but the deviation from zero curvature disappears.

This, to me, says that this can probably be traced to a (small) systematic error on the part of the BAO measurement. That wouldn't be a terrible surprise, as such measurements are notoriously tricky to do right, due to the messiness of galaxies.
 
  • #33
Okay thanks.
These triangles you are talking about aren't in one plane, so their angles don't have to add to 180 degrees. It's sad that the shape can't be imagined, as it is beyond our senses' experiences.
 
  • #34
The triangle methodology is also used with regards to the CMB. However in that usage its quite a bit more complicated. The different
shapes of the universe would
cause different distortions of
the regions of slight
temperature differences.
Like most things scientists study they never rely on just one method. Indeed the WMAP survey is what provided the strongest data as to our shape.
 
  • #35
Chemist@ said:
Okay thanks.
These triangles you are talking about aren't in one plane, so their angles don't have to add to 180 degrees.
I don't know what you mean. In flat space, no matter their orientation, triangles always have angles that add to 180 degrees. You have to be in curved space for that to change.
 
  • #36
Chemist@ said:
Okay thanks.
These triangles you are talking about aren't in one plane, so their angles don't have to add to 180 degrees. It's sad that the shape can't be imagined, as it is beyond our senses' experiences.

Doesn't matter. A plane is just a surface. But a surface is not necessarily a plane. A triangle on a surface that happens to be flat always has angles that add to 180 but a triangle on an arbitrary surface doesn't have to have angles that add to 180.

A surface is just a place where things happen in 2-D. If you were a 2-D creature on a 2-sphere, there is absolutely no way to tell whether you were in a single plane or not; the only way you could tell whether you were on a 2-sphere or on a flat plane is to draw a big triangle and measure the angles.
 
  • #37
boisebrats said:
snip... we, as inferior mankind, through our limited perception of the world, marvel at the impossibility of ideas like "entanglement", the "sole beginning bang of infinite time from nothingness" and even the the philosophical contradiction of the theoretical existence of "totally empty space" ...snip.

My thoughts exactly. Ultimately, cosmology is a philosophical problem with inputs from physics. - CW
 
  • #38
chasw said:
My thoughts exactly. Ultimately, cosmology is a philosophical problem with inputs from physics. - CW
I think you're thinking of cosmogony. Cosmogony is about the origins of the universe. Cosmology is about the evolution of the universe. Cosmology is strongly tied to observation today, and is considered a specific branch of astrophysics. Cosmogony is a bit more speculative, due to a lack of hard data on the subject, and thus most of the arguments regarding it have to be done in the absence of data, which makes the philosophical aspect more important.

That said, all of science uses and relies upon philosophy for its conclusions.
 
  • #39
Thanks Chalnoth for the correction. I was in fact thinking of the origins of the universe and the highly plausible big bang model. For example, the paradox of rapid inflation, at speeds faster than light, boggles the mind.

It seems humans cannot adequately explain what preceeded creation (nothingness?), what triggered it (prime mover?) and how all that matter and energy unfolded in the first few milliseconds. We are too far removed from these unique events to ever move the dialog beyond speculation.

As far as the rest of the universe's story leading up to the present time and beyond, civilization is dependent on a relatively small number of people who are exploring the universe through ever more sophisticated instruments. Even here, the mysteries never seem to end. - CW
 
  • #40
Chalnoth said:
I think you're thinking of cosmogony. Cosmogony is about the origins of the universe. Cosmology is about the evolution of the universe. Cosmology is strongly tied to observation today, and is considered a specific branch of astrophysics. Cosmogony is a bit more speculative, due to a lack of hard data on the subject, and thus most of the arguments regarding it have to be done in the absence of data, which makes the philosophical aspect more important.

That said, all of science uses and relies upon philosophy for its conclusions.

I'll chip in here. I completely agree with Chally's statement here. I often disagree with him on lesser details but this sounds exactly right.

I think it's important not to confuse cosmology with cosmogony (investigating the origin of the universe.)

In pop-literature there is a confusion of the start of expansion with the origin of the universe. We do not know that the start of expansion (popularly called "big bang" though not a good description) coincided with the origin of the universe, or with some "creation out of nothing" event.

There are various models that extend time back before start of expansion. There is reason to hope that we may be able to sort this out and select the best fit model.

I would take issue with what you, Charles, say here: I don't think it's such a good idea to equate (as they do in popular media) the conventional big bang model with "origins of the universe". We do not have a scientific basis of evidence for assuming the two are the same. The conventional model simply breaks down as it approaches the start of expansion, so more robust extensions of it are being developed.

chasw said:
... I was in fact thinking of the origins of the universe and the highly plausible big bang model. For example, the paradox of rapid inflation, at speeds faster than light, boggles the mind. ...

Distances increasing at speeds > c are routine. Most of the galaxies one can observe with telescopes are at distances which are increasing faster than the speed of light. Any distance greater than 14 billion lightyears is doing that. The galaxies are not moving thru space to any great extent, the distances between are simply increasing. Geometry is dynamic and we have no right to expect that stationary objects will not gradually become farther apart.
The current rate of expansion is 1/140 of a percent per million years. This does not sound like much but a distance of 14 billion lightyears growing at that rate is growing at the speed of light. A distance twice that would be growing (proportionally) at twice the speed.
This need not boggle anyone's mind (unless there is some wish to be boggled and a desire to tell people about it)---anyway that's my view.
You could watch the balloon model. Shows galaxies staying still (at fixed lat and long.) and getting farther apart faster than the wiggling photons of light (also shown) can travel.
 
  • #41
As I recall a very recent report, from South Pole Telescope, said that with 95% certainty the curvature was not zero but just a wee bit on the positive side of zero! So that while the U is not infinite (according to them) it is so nearly flat that the hypersphere circumference could be as large as 880 billion lightyears. That is, the 3D analog of a sphere so that if you could stop expansion right now and sail off at light speed in some direction you could travel in a straight line for 880 billion years before you found yourself back home. But it might not be that near flat, or that large--there is a range of uncertainty about the mean curvature.

marcus, I've been reading your posts all day, and while this sort of stuff is certainly far, far beyond my understanding, I'm really enjoying just trying to make sense of them. Mind blowing stuff.

Is there any way you can put this in simpler terms, or any diagrams knocking about that could explain this to a layman like me? Does this report imply the universe is finite and shaped like a sphere and incredibly huge, or am I way off here?
 
  • #42
Hi all.
Total noob here, but extremely interested. Only got as far as 2nd year college physics and that was some 20 years ago, so feel free to explain things to me as if I was a 10 year old.

I've been puzzling over recent remarks that the Universe is spatially flat. Earlier in this thread ...

Mordred said:
Also keep in mind their is no clear consensus if the universe is open or closed. At this point we can only say that it is flat or extremely close to flat.
As mentioned in a month as Marcus mentioned. We will be getting further data.
The sticky thread on the balloon analogy also has tons of useful links. I highly recommend the ones leading to Ned Wrights tutorials. Particularly his FAQ article. Its one of the better articles for those relatively new to cosmology.
Some things to add on the open closed description. If the universe is closed/finite now then its always finite. Same applies to infinite/open.

... which indicates what seems completely logical to me - that if the Universe is flat then it must be infinite. In fact, if the Universe is topologically open then it must be infinite (right? ... at least according to my understanding of the cosmological principal). So, whether it's flat or saddle shaped (negative curvature?) it must be infinite.

Now, what I don't understand is how a Big Bang Universe can be spatially open and infinite. Surely, a singularity is closed and topologically spherical?

Or, in other words, I can picture where a Big Bang could be on a (hyper)sphere, but not on a saddle or plane.

Can somebody explain this to me (like I'm a 10 year old :) ).

Thanks.
 
  • #43
Banana :smile:
 
  • #44
usmhot said:
... which indicates what seems completely logical to me - that if the Universe is flat then it must be infinite. In fact, if the Universe is topologically open then it must be infinite (right? ... at least according to my understanding of the cosmological principal).
Not at all. A torus (doughnut shape) is topologically flat, because you can wrap a flat sheet into a torus without tearing or kinking. Visually, living inside a torus-shaped universe would be rather like the classic video game Asteroids.
 
  • #45
... which indicates what seems completely logical to me - that if the Universe is flat then it must be infinite.


flat SPACE need not mean flat SPACETIME...
 
  • #46
Isn't a torus topologically equivalent to a sphere? Anyway, it's curved and finite and, in particular, unbounded.

Just focused on space though ... flat must be infinite, otherwise it must have boundaries.

So, what shape was the Big Bang? Wasn't it finite and unbounded and closed?

I should have been clearer in my original question ... my problem is with the fact that the Universe must be infinite if it's flat because otherwise it would have to be bounded and would thus break the cosmological principle. So, logically, if it's flat, it must be infinite and it must always be infinite.
 
  • #47
usmhot said:
Isn't a torus topologically equivalent to a sphere?
No. You can't make a sphere out of a flat sheet without tearing. You can make a torus out of a flat sheet without tearing.

usmhot said:
So, what shape was the Big Bang? Wasn't it finite and unbounded and closed?
Unknown, and possibly unknowable. We can only see a small slice of the universe, due to the speed of light limitation. We haven't yet definitively detected any overall spatial curvature in our visible patch, but even if we did, that would only tell us about our visible patch. Imagine, for example, that we detect some amount of positive curvature. That could mean our universe is sort of like the surface of a sphere, or it could mean we're living on a sort of hill on a sheet with lots of hills and valleys.

The only way to get at the answer is to learn the correct model for how our universe began, and then get lucky in that model telling us unambiguously what the shape of our universe must be.

usmhot said:
I should have been clearer in my original question ... my problem is with the fact that the Universe must be infinite if it's flat because otherwise it would have to be bounded and would thus break the cosmological principle. So, logically, if it's flat, it must be infinite and it must always be infinite.
The cosmological principle is just a simple assumption that is probably wrong when you get to large enough scales.
 
  • #48
usmhot said:
my problem is with the fact that the Universe must be infinite if it's flat because otherwise it would have to be bounded and would thus break the cosmological principle. So, logically, if it's flat, it must be infinite and it must always be infinite.
As pointed out before the torus is flat, unbounded and finite.
A different thing is that I believe a 3 dim torus can't be embedded in a Lorentzian manifold so I guess that would leave us with the "flat space means infinite space" assumption again.
 
  • #49
Chalnoth said:
The cosmological principle is just a simple assumption that is probably wrong when you get to large enough scales.
I don't think it is a simple assumption that is probably wrong, it is "the" assumption that sustains the LCDM model(including the flat space, inflation and dark matter and dark energy assumptions) and GR's FRW metrics.
If it is indeed wrong all that has to be questioned.
are you influenced by the Planck data confirming anomalies at large scales to say that?
 
  • #50
TrickyDicky said:
I don't think it is a simple assumption that is probably wrong, it is "the" assumption that sustains the LCDM model(including the flat space, inflation and dark matter and dark energy assumptions) and GR's FRW metrics.
It only has to hold within the observable universe for this to be the case. Once we start going beyond the observable universe, well, pretty much anything goes. We expect that the cosmological principle must hold significantly beyond the observable universe primarily because if it didn't, we would expect to see some deviation within it as well. But there's no reason to believe it holds out to infinity.

TrickyDicky said:
are you influenced by the Planck data confirming anomalies at large scales to say that?
Not at all. I would have told you the exact same thing five years ago.
 
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