The size of the universe confuses me.

[Iroscato]

Forgive if I sound slightly retarded with asking this question, but if there's one place I should get an answer it's here.
The true size of the universe, as I understand it, is far, far larger than what we can observe, about 13.7 billion light years away. OK, that's fair enough. Now, if the universe extends to much further out than that, surely that means it is expanding faster than light? If it expanded at lightspeed, it would be about 13 billion lightyears across, as I understand it.

Now, since travelling at faster than the speed of light is meant to be, like, impossible and all that shit, what's going on? Am I woefully misunderstanding something here? So, my question is basically, how can the universe be expanding faster than light?

[Lord Zentei]

It's impossible for anything to move faster than light. What that actually means is that no thing can move (i.e. pass through space during time) faster than light - if you organize a fair race between anything and light, light always wins, or at least breaks even.

However, space itself can expand at any "speed". This is what causes the universe to expand; it's not that things are hurtling through space after a huge explosion - it's space itself that is exploding, or rather expanding.

Moreover: space expands behind the object after the light is emitted, and in front of it as it struggles to reach Earth, so the distance the light has to travel is greater than the speed of light multiplied by the time elapsed.

[Iroscato]

It's impossible for anything to move faster than light. What that actually means is that no thing can move (i.e. pass through space during time) faster than light - if you organize a fair race between anything and light, light always wins, or at least breaks even.

However, space itself can expand at any "speed". This is what causes the universe to expand; it's not that things are hurtling through space after a huge explosion - it's space itself that is exploding, or rather expanding.

Moreover: space expands behind the object after the light is emitted, and in front of it as it struggles to reach Earth, so the distance the light has to travel is greater than the speed of light multiplied by the time elapsed.

You see, I think I suffer from a similiar problem to those people who think of the big bang as a literal bang

[Lord Zentei]

It's probably due to all those animations we seen in sundry programmes which try to explain it. Also, due to misinformation from guys like Banana Man and others, but the first reason doesn't help.

Fun fact: it was originally a critic of the theory (I think it was Fred Hoyle) who coined the term "Big Bang" as a pejorative. His own Steady State theory was the main rival. That pejorative term simply stuck.

[mr friendly guy]

The expansion of the universe was explained to me as (and I am paraphrasing here)... like a balloon being blown up with an insect walking across it representing light. The insect is travelling between two points you have marked on the balloon before it started being blown up. On the surface of the balloon nothing can go faster than the insect, yet the distance between the two points get longer before the insect can transverse it, ergo the universe is expanding "faster" than light.

[cosmicalstorm]

Are you talking about the observable universe or the entire universe?

Cosmos At Least 250x Bigger Than Visible Universe, Say Cosmologists

The universe is much bigger than it looks, according to a study of the latest observations.

When we look out into the Universe, the stuff we can see must be close enough for light to have reached us since the Universe began. The universe is about 14 billion years old, so at first glance it's easy to think that we cannot see things more than 14 billion light years away.

That's not quite right, however. Because the Universe is expanding, the most distant visible things are much further away than that. In fact, the photons in the cosmic microwave background have travelled a cool 45 billion light years to get here. That makes the visible universe some 90 billion light years across.

That's big but the universe is almost certainly much bigger. The question than many cosmologists have pondered is how much bigger. Today we have an answer thanks to some interesting statistical analysis by Mihran Vardanyan at the University of Oxford and a couple of buddies.

Obviously, we can't directly measure the size of the universe but cosmologists have various models that suggest how big it ought to be. For example, one line of thinking is that if the universe expanded at the speed of light during inflation, then it ought to be 10^23 times bigger than the visible universe.

Other estimates depend on a number factors and in particular on the curvature of the Universe: whether it is closed, like a sphere, flat or open. In the latter two cases, the Universe must be infinite.

If you can measure the curvature of the Universe, you can then place limits on how big it must be.

It turns out that in recent years, astronomers have various ingenious ways of measuring the curvature of the Universe. One is to search for a distant object of known size and measure how big it looks. If it's bigger than it ought to be, the Universe is closed; if it's the right size, the universe is flat and if it's smaller, the Universe is open.

Astronomers know of one type of object that fits the bill: waves in the early universe that became frozen in the cosmic microwave background. They can measure the size of these waves, called baryonic acoustic oscillations, using space observatories such as WMAP.

There are also other indicators, such as the luminosity of type 1A supernovas in distant galaxies.

But when cosmologists examine all this data, different models of the Universe give different answers to the question of its curvature and size. Which to choose?

The breakthrough that Vardanyan and pals have made is to find a way to average the results of all the data in the simplest possible way. The technique they use is called Bayesian model averaging and it is much more sophisticated than the usual curve fitting that scientists often use to explain their data.

A useful analogy is with early models of the Solar System. With the Earth at the centre of the Solar System, it gradually became harder and harder to fit the observational data to this model. But astronomers found ways to do it by introducing ever more complex systems, the wheels-within-wheels model of the solar system.

We know now that this approach was entirely wrong. One worry for cosmologists is that a similar process is going on now with models of the Universe.

Bayesian model averaging automatically guards against this. Instead of asking how well the model fits the data, its asks a different question: given the data, how likely is the model to be correct. This approach is automatically biased against complex models--it's a kind of statistical Occam's razor.

In applying it to various cosmological models of the universe, Vardanyan and co are able to place important constraints on the curvature and size of the Universe. In fact, it turns out that their constraints are much stricter than is possible with other approaches.

They say that the curvature of the Universe is tightly constrained around 0. In other words, the most likely model is that the Universe is flat. A flat Universe would also be infinite and their calculations are consistent with this too. These show that the Universe is at least 250 times bigger than the Hubble volume. (The Hubble volume is similar to the size of the observable universe.)

That's big, but actually more tightly constrained than many other models.

And the fact that it comes from such an elegant statistical method means this work is likely to have broad appeal. If so, it may well end up being used to fine tune and constraint other areas of cosmology too.

[Rabid]

Help me there...

They say in one sentence that the Universe is infinite ; and in following one that it has a finite size ( ~250x the size of the observable universe) :

They say that the curvature of the Universe is tightly constrained around 0. In other words, the most likely model is that the Universe is flat. A flat Universe would also be infinite and their calculations are consistent with this too. These show that the Universe is at least 250 times bigger than the Hubble volume. (The Hubble volume is similar to the size of the observable universe.)

(bolding mine)


Is this some Topology trick (like, you reach one "side" and end up on the opposite one), or just a confusing wording ?

[Surlethe]

Here's their paper. http://arxiv.org/abs/0901.3354 Judge for yourself

(Actually, I'm afraid that I don't have the time to do more than skim the paper, so I can't say anything confidently about it. I would guess, however, that what they're referring to is the difference between (1) implying the universe has infinite extent and (2) setting an observational lower bound on the size of the universe. In other words, the way I skimmed their conclusion, the universe is very likely to be at least 250 times larger than the observable universe.)

Maybe later today I will comment on the OP.

[Eternal_Freedom]

I think it's just confusing wording. They have apparently got calculations showing that the universe is at least 250x the observable one, but that if it is a flat universe, then it should be infinite.

That's what I get from reading it anyway.

[Rabid]

Topology : Y U GOTTA MAKE MA HEAD ASPLODE ?!


What does "infinite" mean ? Does it mean "without border", or something ? Because otherwise, instinctively I would be coming to the conclusion that 1) if the universe is infinite in size and 2) is always expanding then it means that even during the Big Bang (which would be the point at which the Universe was the most dense, so dense that it fucked space-time and there wasn't really a "before" as much as I understand the Theory) the universe was already infinite.

HOWEVER, it is commonly said in documentaries that during the Inflation, the universe went from the size of an atom (or was it the planck scale ?) to the size of an orange in X amount of time. So, is it an absolute statement, or just a way for the layman to visualize the rate of expansion of this already infinite "space-time" ?

[starslayer]

There are three possible curvatures for the universe in GR: flat, open, or closed (mathematically, the curvature could be zero, negative, or positive). Flat and open universes are infinite in size, while closed ones are finite but unbounded, like the surface of the Earth. The error bounds on the curvature of the universe do not preclude any of the three possibilities yet; however, it is more likely open than closed, and whichever it ends up being, we know the universe is very, very close to being flat. It could be perfectly flat, but this is unlikely, since a truly flat universe is an extreme case.

What does "infinite" mean ? Does it mean "without border", or something ? Because otherwise, instinctively I would be coming to the conclusion that 1) if the universe is infinite in size and 2) is always expanding then it means that even during the Big Bang (which would be the point at which the Universe was the most dense, so dense that it fucked space-time and there wasn't really a "before" as much as I understand the Theory) the universe was already infinite.

Yes, the universe in full was infinite as long as it has existed, if it is open or flat. The observable universe, which those documentaries are almost always referring to, has obviously always been finite. In an infinite universe, even with FTL, you can fly in any direction you please forever, and never come back to the same spot or hit an edge or boundary of any kind.

[Surlethe]

Hey starslayer, why can't the universe be flat or negatively curved and yet closed, like, say, a flat torus? [More explicitly, you ought to be able to take a quotient of a four dimensional de Sitter spacetime by a discrete subgroup of PSU(3,1).] Are there topological obstructions implied by the field equations?

[Surlethe]

You want to think of the universe in terms of a scale factor, which is a function of time. Say the scale factor at -12 billion years from now is 1%. What this means is as follows. Take two stationary observers who have not moved. Right now, they're some distance apart. 12 billion years ago, they're 1% as far apart as they are now. Maybe 20 billion years in the future, the scale factor is 150%. Then they're half again as far apart in 20 billion years as they are now.

What you can do is write down the GR field equations with this scale factor plopped in front of a constant metric, solve, and you get a differential equation for the scale factor. This differential equation is a model for the expansion/contraction of the universe.

[Simon_Jester]

Topology : Y U GOTTA MAKE MA HEAD ASPLODE ?!

What does "infinite" mean ? Does it mean "without border", or something ? Because otherwise, instinctively I would be coming to the conclusion that 1) if the universe is infinite in size and 2) is always expanding then it means that even during the Big Bang (which would be the point at which the Universe was the most dense, so dense that it fucked space-time and there wasn't really a "before" as much as I understand the Theory) the universe was already infinite.

HOWEVER, it is commonly said in documentaries that during the Inflation, the universe went from the size of an atom (or was it the planck scale ?) to the size of an orange in X amount of time. So, is it an absolute statement, or just a way for the layman to visualize the rate of expansion of this already infinite "space-time" ?

The universe was never necessarily a geometric point, if we have a flat or open universe. I think the documentaries are just going off of density of the universe (which can be calculated for a given point in time), and possibly the mass of the observable universe. Know how much is in the observable universe and how dense it was at a certain time after the Big Bang, and you have a volume... but it doesn't give the volume of the stuff you can't see, since you don't know how much of it there is.

Hey starslayer, why can't the universe be flat or negatively curved and yet closed, like, say, a flat torus? [More explicitly, you ought to be able to take a quotient of a four dimensional de Sitter spacetime by a discrete subgroup of PSU(3,1).] Are there topological obstructions implied by the field equations?

I can't really sit down and math it out; at a guess the problem arises when you factor in isotropy. If the universe has the same curvature in all directions, it greatly restricts the range of possible topologies.

...I think.

[Havok]

Head assploding indeed.

Isn't there a theory, that what we think of as our universe, is actually, like galaxies, one of a massive number of 'universes' in a bigger universe, and the issue is that the light required to see them just hasn't traversed between them yet?

Then there is the mind boggling question of what the universe is expanding INTO.

I hate this forum.

[starslayer]

Hey starslayer, why can't the universe be flat or negatively curved and yet closed, like, say, a flat torus? [More explicitly, you ought to be able to take a quotient of a four dimensional de Sitter spacetime by a discrete subgroup of PSU(3,1).] Are there topological obstructions implied by the field equations?

This is flat in terms of the FRW metric, that is, ds2 = -c2dt2 + a2(t)*(dr2/(1-kr2)+r2dΩ2), where k is the curvature, a is the scale factor, and dΩ2 is the spherical anglular element. No matter what k is, this metric does not generate a torus. Instead, if k is 0, it's just flat Minkowski spacetime. If k is negative, you get hyperbolic spacetime, and if k is positive, you get an elliptical spacetime.

The EFEs themselves don't really care about the topology of spacetime; you can make any spacetime you like if you the construct the metric correctly. However, the standard assumptions of cosmology (that the universe is homogenous and isotropic, and that it is filled with a perfect fluid) generate the FRW metric, and do so fairly directly, actually. It's really the "homogenous and isotropic" criterion that torpedoes the possibility of the universe being a torus, as Simon mentioned.

By the way, I'm not familiar with symmetry groups, etc. yet, so the more advanced topological stuff is beyond me at this point.

[Lord Zentei]

That's not quite right, however. Because the Universe is expanding, the most distant visible things are much further away than that. In fact, the photons in the cosmic microwave background have travelled a cool 45 billion light years to get here. That makes the visible universe some 90 billion light years across.

That's not quite right either. The point at which the CMB was emitted is 45 billion light years distant, but the light didn't travel all of that distance, since space also expanded behind the light as it traveled.

Nit pick, I know. But the article itself is nitpicking, so I felt it appropriate.

[Iroscato]

This is flat in terms of the FRW metric, that is, ds2 = -c2dt2 + a2(t)*(dr2/(1-kr2)+r2dΩ2), where k is the curvature, a is the scale factor, and dΩ2 is the spherical anglular element. No matter what k is, this metric does not generate a torus. Instead, if k is 0, it's just flat Minkowski spacetime. If k is negative, you get hyperbolic spacetime, and if k is positive, you get an elliptical spacetime.

Er, yeah. I totally agree.
So, basically, space itself is expanding? And it can travel at any speed it wants and it's expanding into an infinite space and...and...
Christ I need an aspirin. This is indeed, to quote Havok, "Head assploding".

[Surlethe]

The EFEs themselves don't really care about the topology of spacetime; you can make any spacetime you like if you the construct the metric correctly. However, the standard assumptions of cosmology (that the universe is homogenous and isotropic, and that it is filled with a perfect fluid) generate the FRW metric, and do so fairly directly, actually. It's really the "homogenous and isotropic" criterion that torpedoes the possibility of the universe being a torus, as Simon mentioned.

I think I get it. Do physicists (cosmologists) use "homogeneous" and "isotropic" in the same way mathematicians do? (If I'm not screwing up my definitions, a manifold is homogenous provided you can get from any point to any other point via isometry, and isotropic provided you can get from any tangent vector to any other tangent vector via isometry.)

By the way, I'm not familiar with symmetry groups, etc. yet, so the more advanced topological stuff is beyond me at this point.

I don't actually know if the construction I implied works I'm motivated by the two-dimensional case where a simple de Sitter spacetime is in some sense dual to hyperbolic space. (Hyperbolic space is the set of timelike rays in a Minkowski vector space, while de Sitter space is the set of spacelike rays.) You can "roll" hyperbolic space by discrete subgroups of the Lorentz group the same way you can "roll" Euclidean space by discrete subgroups of the Euclidean group (translations and rotations) to get a torus. In the hyperbolic case, you can do this for any two-dimensional surface of genus larger than 1. I was thinking that something very similar should be the case for de Sitter space (but I don't know if you can do similar quotients of four-dimensional hyperbolic space).

[Simon_Jester]

"Homogeneous" as in:

"Over sufficiently large scales, the density of matter in the universe is roughly constant."

"Isotropic" as in:

"Over sufficiently large scales, the distribution of mass in the universe does not depend on the angle with which one travels away."

This makes it awkward to construct 'toroidal' geometries with different curvature depending on whether you travel along the X axis or the Y axis, so to speak.

[Surlethe]

Okay, everybody: space is not expanding into anything. Distances are just getting bigger. That's it.

Repeat after me: the big bang happened everywhere, not at a point. The universe is getting bigger, not expanding into anything.

[Simon_Jester]

Gotcha.

My comments about isotropy stand, though.

Basically, I think the cosmological community would be stunned to discover evidence that the curvature of the universe was different in different directions by even a slight degree.

[Lord Zentei]

This is flat in terms of the FRW metric, that is, ds2 = -c2dt2 + a2(t)*(dr2/(1-kr2)+r2dΩ2), where k is the curvature, a is the scale factor, and dΩ2 is the spherical anglular element. No matter what k is, this metric does not generate a torus. Instead, if k is 0, it's just flat Minkowski spacetime. If k is negative, you get hyperbolic spacetime, and if k is positive, you get an elliptical spacetime.

Er, yeah. I totally agree.
So, basically, space itself is expanding? And it can travel at any speed it wants and it's expanding into an infinite space and...and...
Christ I need an aspirin. This is indeed, to quote Havok, "Head assploding".

It's not really expanding "into" anything, since it's not occupying any "space" - it is space. It's perhaps better to think of it as inflation: the "value" of space between any two objects is getting greater. Since it's not expanding "through" anything, we have to speak of the scale factor of space instead, i.e. the relative distance between any two objects as a function of time. It's only through gravity and the other fundamental forces pulling things together that everything isn't drifting apart, even when they're not moving through space with respect to each other. Over very great distances, gravity isn't strong enough for this, hence the receding distant galaxies.

The expansion of space isn't arbitrary, it's constrained by its contents. The rate of expansion is a function of the composition of the universe: energy+matter and dark energy (which remains mysterious).


EDIT: great, just great. I walk away for a couple of minutes, and get ninja'd by Surlethe as a result.

[Surlethe]

Gotcha.

My comments about isotropy stand, though.

Basically, I think the cosmological community would be stunned to discover evidence that the curvature of the universe was different in different directions by even a slight degree.

Sorry, that wasn't aimed at you.

So you do use the terms differently. Maybe it boils down to the same thing in the end --- in a universe filled with a constant-density fluid that's the same at every point in every direction (COPERNICAN HERESY!), it follows from the field equations that the metric must make space an isotropic manifold.

(edit @Zentei )

[Kuroneko]

A quick comment; not enough time to go deeper.

... why can't the universe be flat or negatively curved and yet closed, like, say, a flat torus?

There really isn't any reason. One can physically motivate some restrictions on orientability (e.g., neutrino violates of P-symmetry mean we should have space-orientability), but that obviously doesn't exclude the flat torus.

This is flat in terms of the FRW metric, that is, ds2 = -c2dt2 + a2(t)*(dr2/(1-kr2)+r2dΩ2), where k is the curvature, a is the scale factor, and dΩ2 is the spherical anglular element. No matter what k is, this metric does not generate a torus. Instead, if k is 0, it's just flat Minkowski spacetime. If k is negative, you get hyperbolic spacetime, and if k is positive, you get an elliptical spacetime.

Not so! In fact, it's easy to see that any topological restrictions are going to be very loose. The standard FRW universe is a warped product of R×S³, with the above metric (k = +1). Take the sphere and identify antipodal points, making it a real projective space. Then your spacetime has topology R×SO(3) instead (real projective space), and it doesn't break anything, because GTR is local, so initial data on an SO(3)-surface corresponds to initial data on an S³-surface of the canonical FRW, and "isotropic and homogeneous" is not much of a requirement. In coordinates where the closed FRW used the round metric, we get the same thing:
ds² = -dt² + a²(t)[dχ² + sin²χ(dθ² + sin²θ dφ²)]
except that S³ would use φ between 0 and 2π, but SO(3) would use φ between 0 and π. In coordinate form, solution nearly blind to the topology change.

It's really the "homogenous and isotropic" criterion that torpedoes the possibility of the universe being a torus, as Simon mentioned.

But Simon is not correct, because the torus is also homogeneous and isotropic (locally!).

I think I get it. Do physicists (cosmologists) use "homogeneous" and "isotropic" in the same way mathematicians do? (If I'm not screwing up my definitions, a manifold is homogenous provided you can get from any point to any other point via isometry, and isotropic provided you can get from any tangent vector to any other tangent vector via isometry.)

This generally refers to the initial (stress-energy) conditions themselves, and is therefore a local requirement. Though the flat torus is not an isotropic manifold, this only shows up in the global structure, and is not generally what's meant by physicists.