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

In summary: Below is a picture of the flat universe:http://img607.imageshack.us/img607/412/55426705.gifThe 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?I detect your misunderstanding of how a flat universe works. The arrow is not pointing at the end of the universe, it is pointing at the smallest dimension of the universe. Anywhere on the flat universe
  • #1
Chemist@
115
1
How certainly is the universe flat? Is is absolutely approved or not?
If yes, what will cause the big crunch?
 
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  • #2
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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  • #3
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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  • #4
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'
 
  • #5
In the thread I mentioned above Marcus is one of the best qualified to explain how to use it.
 
  • #6
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 [Broken]
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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  • #7
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.
 
  • #8
From which year are these data?

How would a flat closed universe look like?
 
  • #9
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 [Broken]
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 [itex]H_0[/itex], 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.
 
<h2>1. What is the current accepted shape of the universe?</h2><p>The current accepted shape of the universe is flat. This means that the universe has a Euclidean geometry and has a constant curvature of zero.</p><h2>2. How do scientists determine the shape of the universe?</h2><p>Scientists determine the shape of the universe through observations and measurements of the cosmic microwave background radiation. This radiation is a remnant of the early universe and its patterns can reveal the curvature of the universe.</p><h2>3. What is the significance of the flatness of the universe?</h2><p>The flatness of the universe has significant implications for the ultimate fate of the universe. A flat universe indicates that the expansion of the universe will continue forever, leading to a "heat death" scenario where all matter and energy are evenly distributed and the universe reaches a state of maximum entropy.</p><h2>4. What is the Big Crunch theory?</h2><p>The Big Crunch theory suggests that the universe will eventually stop expanding and start contracting, leading to a collapse of the universe. This would result in a "big crunch" where all matter and energy are compressed into a singularity.</p><h2>5. Is the Big Crunch still a possibility in a flat universe?</h2><p>Currently, the Big Crunch theory is not supported by observational evidence. In a flat universe, the expansion is expected to continue forever, making a Big Crunch scenario unlikely. However, the possibility of a Big Crunch cannot be completely ruled out as our understanding of the universe is constantly evolving.</p>

1. What is the current accepted shape of the universe?

The current accepted shape of the universe is flat. This means that the universe has a Euclidean geometry and has a constant curvature of zero.

2. How do scientists determine the shape of the universe?

Scientists determine the shape of the universe through observations and measurements of the cosmic microwave background radiation. This radiation is a remnant of the early universe and its patterns can reveal the curvature of the universe.

3. What is the significance of the flatness of the universe?

The flatness of the universe has significant implications for the ultimate fate of the universe. A flat universe indicates that the expansion of the universe will continue forever, leading to a "heat death" scenario where all matter and energy are evenly distributed and the universe reaches a state of maximum entropy.

4. What is the Big Crunch theory?

The Big Crunch theory suggests that the universe will eventually stop expanding and start contracting, leading to a collapse of the universe. This would result in a "big crunch" where all matter and energy are compressed into a singularity.

5. Is the Big Crunch still a possibility in a flat universe?

Currently, the Big Crunch theory is not supported by observational evidence. In a flat universe, the expansion is expected to continue forever, making a Big Crunch scenario unlikely. However, the possibility of a Big Crunch cannot be completely ruled out as our understanding of the universe is constantly evolving.

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