Shape of the Universe: Is it Infinite or Finite?

[arupel]

Just like to get an idea of what people currently think what the shape of the universe is.

Since the curvature is likely zero, does this mean that the universe is infinite.

Also, I get the idea that the size of the universe, if has one, extends beyond the light cone. How is this possible?

 

[Bandersnatch]

Just like to get an idea of what people currently think what the shape of the universe is.

The consensus is: if we keep all the assumptions used in describing the observable universe, then the universe as a whole is consistent both with being infinite in extent, and with being finite but very large.

The assumptions concern homogeneity and isotropy, i.e. the cosmological principle. It is perfectly possible for the laws of physics to differ in other, causally disconnected regions of the universe, in which case anything goes. But if we were to assume that they don't change, and everything does look pretty much the same as in our patch of visible universe, then the size is determined by curvature.

Curvature measurements keep narrowing down with consecutive astrometric missions, and seem to zero-in on the flat case. However, by the nature of any and all measurements, it is impossible to obtain a result not burdened with uncertainty, so there will be always a range of possible curvatures indicated, and as a result - a range of sizes (in case of positive curvature). The error bars currently allow for all three of curvature families - open, flat and closed (so, both finite and infinite). However, the current precision let's us estimate the smallest possible radius of the curvature as 205 billion light years (using the PLANCK 2015 results for $H_0=67.8 +/- 0.9$ and $\Omega=0.000 +/- 0.005$.

Also, I get the idea that the size of the universe, if has one, extends beyond the light cone. How is this possible?

For a similar reason why the ocean extends beyond the horizon. You are limited to what you see by where you are as an observer. If you change your vantage point on the ocean e.g. by sailing a few metres west, you'll see a different patch than before. Same with the light cones - if you step over a light year towards the Alpha Centauri, your observable universe will encompass a different region of the whole.By the way, be mindful of the thread level tags. These are not meant to represent the poster's perceived complexity of the subject, but their prior level of knowledge, and the level of knowledge they'd like to receive answers at. This looks like a B, maybe I thread, judging by the question. Marking it A may result in: 1) answers with more maths than words, and 2) lack of replies, as everybody waits for that one expert to show up :)

 

[Chronos]

But, barring superluminal travel, by the time you move a light year towards alpha centauri, the particle horizon of the observable universe will also receed at least another light year so you won't see anything more than you could have seen had you just stayed put instead of moving towards alpha centauri.

 

[Bandersnatch]

That's not correct, Chronos - you will e.g. see light from AC, or light from CMB from the direction of AC one year earlier than had you stayed at home.

 

[Carlos L. Janer]

There's something I don't really get. If our Universe is expanding and becoming more dilute and red shifted, its baryonic, radiation, dark matter and dark energy content should be changing with time at different rates and I guess (although I may be wrong) that its total energy content should be changing. How is it then possible that the laws of Physics don't change as time passes? or, more generally, how is it possible that physical laws are invariant with respect to Poincare's group? If an instataneous space translation takes place (it is a possible Poincare translation), would we see another Universe with the same set of natural laws as ours? What do we really mean when we use the word 'Universe'?

My question may be naive, but I don't really understand it (I don't know anything about Cosmology).

 

[bapowell]

Since the curvature is likely zero, does this mean that the universe is infinite.

Not necessarily. Zero curvature is consistent with a toroidal universe.

 

[rootone]

There's something I don't really get. If our Universe is expanding and becoming more dilute and red shifted ...

The observed red shift is partially a doppler effect and partially the effect of that the most distant galaxies we can see are traveling away from us at close to light speed.
If you could magically teleport yourself to one of those very distant galaxies the light of it's stars locally will not be redshifted.
If you then looked back at the milky way galaxy then that would appear redshifted instead.
(just in principal of course, you might find that after your teleportation the distant galaxy is no longer in existence as such, It may have merged with other galaxies or have become mainly consisting of dead stars,since what you originally observed before teleporting was a galaxy that existed billions of years ago.)

 

[Chalnoth]

Just like to get an idea of what people currently think what the shape of the universe is.

Since the curvature is likely zero, does this mean that the universe is infinite.

I don't think it will ever be possible to say that the curvature is likely zero (barring some really strong theoretical arguments with independent supporting evidence). As Bandersnatch mentioned, there will always be some error in the measurement. We may some day be able to say that the curvature is non-zero, but it will never be possible to have perfect accuracy on measuring the curvature.

The most that we can say is that at the current time, our universe is very close to flat.

Unfortunately, that doesn't say anything one way or the other about our universe being infinite. As bapowell mentioned, we could live in a toroidal universe, which is both flat and finite. There's also the possibility that if we have some non-zero curvature that that is simply a local effect: the universe could still be flat on scales much larger than the observable universe.

Also, I get the idea that the size of the universe, if has one, extends beyond the light cone. How is this possible?

The light cone just sets how far signals travel. It doesn't say anything about what does or does not exist. For one, it's entirely possible for the dynamics of the early universe to be such that systems were in causal contact (that is, they could send multiple photons between one another), and then the subsequent expansion brought them out of causal contact.

This is in fact one of the motivations behind cosmic inflation: one of the problems of the classical big bang theory is that in the early universe, objects separated from one another by more than about a degree or so on the sky could never have communicated before the CMB was emitted. So why are those regions at nearly the same temperature (typically within about one part in 100,000 in temperature)? Inflation solves this problem by proposing a different expansion history which brings those regions in causal contact earlier-on.

 

[rollete]

The concept of the universe having a "shape", while fascinating (and depressing), has always sort of flown over my head.

One question to those in the know: is this hypothetical "shape" or curvature understood as a property of spacetime geometry or is it something else beyond that?

 

[Chalnoth]

The concept of the universe having a "shape", while fascinating (and depressing), has always sort of flown over my head.

One question: is this hypothetical "shape" or curvature understood as property of spacetime geometry or is it something else?

There are two separate components of the shape of the universe:
1. Does the universe wrap back on itself? In what way?
2. What is the local curvature of the universe?

The first is a global property of the universe, and unfortunately may be unmeasurable. If the universe wrapped back on itself relatively nearby, then we could detect it. But it appears that if it does wrap back on itself, it does this so far away that we won't ever be able to tell.

The second is measurable, and it appears the answer is that the curvature within our observable universe is very close to flat. This is a local property of the spacetime geometry.

 

[rollete]

Ah, good answer. Cleared up some things in my mind.

1. Does the universe wrap back on itself? In what way?

The first is a global property of the universe, and unfortunately may be unmeasurable. If the universe wrapped back on itself relatively nearby, then we could detect it. But it appears that if it does wrap back on itself, it does this so far away that we won't ever be able to tell.

This is something I was wondering about. If it is a global property of the universe why would we even think that we might be capable of measuring it? How could such an overarching property be detected? Is it hypothesized that the local curvature of spacetime might give a clue about the shape of the universe?

As far as I can tell, there's no reason to assume that one thing has anything to do with the other. I could be wrong since I'm not aware of all the data available.

 

[rootone]

How could such an overarching property be detected?.

I guess that it would need super-duper telescopes that could produce a high resolution image of the back of your head.

 

[Chalnoth]

This is something I was wondering about. If it is a global property of the universe why would we even think that we might be capable of measuring it? How could such an overarching property be detected? Is it hypothesized that the local curvature of spacetime might give a clue about the shape of the universe?

If it wrapped back on itself reasonably close to the horizon, then we could measure it. It doesn't, so we can't.

For example, if it wrapped back on itself close enough, then parts of the CMB would repeat themselves. Further away, there are clever methods using measurements of very long wavelengths.

The curvature can potentially relate to whether the universe wraps back on itself. For example, if the overall shape of our universe was that of the surface of a sphere, then there would be local curvature as well. Current measurements on the curvature show that if the universe has this shape, the radius of this sphere is more than a trillion light years.

 

[PeterDonis]

The observed red shift is partially a doppler effect and partially the effect of that the most distant galaxies we can see are traveling away from us at close to light speed.

Um, interpreting the redshift as a Doppler effect is the same as interpreting it as due to the recession velocity of distant galaxies.

The Doppler effect interpretation can also be somewhat misleading, because the light we see from distant galaxies was emitted a long time ago, and the motion of that galaxy relative to us when the light was emitted will be different from its motion relative to us "now". Also, the "motion" in question is not an ordinary "relative velocity" in the SR sense; it's a coordinate velocity in FRW coordinates. There isn't an SR-style inertial frame that covers both us and the distant galaxy.

An alternate interpretation of the redshift, which I prefer, is that it tells you by what factor the universe has expanded between the light being emitted and now. The expansion factor is $1 + z$, where $z$ is the redshift. For example, a redshift of $z = 1$ means the universe has expanded by a factor of $2$ since the light was emitted.

 

[Bandersnatch]

Current measurements on the curvature show that if the universe has this shape, the radius of this sphere is more than a trillion light years.

Can you give me a reasoning behind the trillion ly number? I get 205 billion from the numbers provided in post #2.

 

[Chalnoth]

Can you give me a reasoning behind the trillion ly number? I get 205 billion from the numbers provided in post #2.

You're right. I screwed up my back-of-the envelope estimate.

 

[Carlos L. Janer]

Is my previous post nonsense?

 

[PeterDonis]

its total energy content should be changing. How is it then possible that the laws of Physics don't change as time passes?

Because the laws of physics don't require global conservation of energy in curved spacetime. Sean Carroll has a good article about this:

http://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/

how is it possible that physical laws are invariant with respect to Poincare's group?

They are locally invariant with respect to the Poincare group. In a curved spacetime there is no such thing as a global Poincare transformation.

If an instataneous space translation takes place (it is a possible Poincare translation)

In flat spacetime, yes. Not in curved spacetime.

 

[Carlos L. Janer]

Thanks for your post. I just have one question. I thought that the general consensus was that our Universe was flat.

 

[Chalnoth]

Thanks for your post. I just have one question. I thought that the general consensus was that our Universe was flat.

It's close to flat for sure. See the more detailed answers to this above.

 

[Bandersnatch]

Thanks for your post. I just have one question. I thought that the general consensus was that our Universe was flat.

When talking about flatness of the universe, the spatial flatness is meant. PeterDonis is talking about space-time.

 

[Carlos L. Janer]

I'm not sure if I got it right: the universe is expanding because its energy-momentum tensor is non-null and, therefore, Einstein's curvature tensor is also non-null (so space-time is curved).

 

[PeterDonis]

the universe is expanding because its energy-momentum tensor is non-null and, therefore, Einstein's curvature tensor is also non-null (so space-time is curved).

Close. The universe is expanding because of the initial conditions at the Big Bang. The change in the expansion rate with time is due to the stress-energy present in the universe. The spacetime of the universe is curved because the stress-energy tensor is nonzero; but this would be true even if the universe were not expanding (because of different initial conditions).

 

[Carlos L. Janer]

OK, thanks again.

 

[Khashishi]

Not necessarily. Zero curvature is consistent with a toroidal universe.

Yeah, but if you assume global isotropy, then you rule out a torus, and any other finite shapes at zero curvature. Of course, we don't know if the universe is globally isotropic or even homogeneous.

 

[TROU]

Just like to get an idea of what people currently think what the shape of the universe is.

Since the curvature is likely zero, does this mean that the universe is infinite.

Also, I get the idea that the size of the universe, if has one, extends beyond the light cone. How is this possible?

Hi. Fascinating discussion. I'm new to this forum and I picked this post because you say that space is likely flat or 'Euclidean'. I would agree, but what leads you to believe it is if I may ask?

 

[bapowell]

Hi. Fascinating discussion. I'm new to this forum and I picked this post because you say that space is likely flat or 'Euclidean'. I would agree, but what leads you to believe it is if I may ask?

Welcome to PF! We are able to measure the curvature of the observable universe using data from the cosmic microwave background. These data show that the observable universe is close to being flat, but we can't tell if it's exactly flat or slightly curved. I believe the latest measurements show that the universe is flat to within a percent or so.

 

[Chronos]

Our best evidence to date for the flatness of space [i.e. Eucldean geometry] comes mainly from CMB data via Planck and WMAP, which as bapowell noted, gives us highly accurate measurements of curvature. These measurements are further affirmed by independent surveys from other studies [e.g., BOSS and SDSS]. These enable us to approximate the mass contained within very large volumes of the universe and which directly affects the curvature, or flatness, of space.

 

[bapowell]

Thanks for your reply. On the microwave background radiation; Aside from it being used to estimate the curvature, and being a pillar of the 'Big Bang' theory; doesn't the measured uniformity in the radiation seem counter-intuitive to the observed existence of galactic clusters and super clusters?

Great question! The answer is "no" -- while the CMB is indeed very uniform, it's not perfect. There are tiny fluctuations in the temperature at 1 part in 100,000 that are understood to be the primordial "seeds" of the galaxies and galaxy clusters that we observe today. Though tiny at the time the CMB was formed, these inhomogeneities eventually grew as gravitational instabilities into bound structures. Regarding even larger structures, like super clusters, there are some hints that the CMB lacks statistical isotropy on the largest length scales: there are some curious "anomalies" regarding the size of fluctuations on the largest scales and the alignment of the multipole vectors that describe these fluctuations.

 

[rootone]

Thanks for your reply. On the microwave background radiation; Aside from it being used to estimate the curvature, and being a pillar of the 'Big Bang' theory; doesn't the measured uniformity in the radiation seem counter-intuitive to the observed existence of galactic clusters and super clusters? In other words the universe seems too clumpy in its distribution of matter. Just a thought.

Although the CMB is nearly uniform it isn't absolutely completely uniform, there are hotter and colder spots.
It can be argued that these tiny initial variations correspond to areas of very slightly different density, and that these were the seeds of the large scale structures which we observe.