Is the universe still expanding?

[Mike2]

Mike, I think it's pretty presumptuous to assume that our traditional notions of cause and effect apply to the beginning of time. Even if they did, I don't see any reason why the "cause" should have to exist in our spacetime. If either of those assumptions were wrong, so would be your conclusions.

It's really a waste of time to debate about it, though. We have about as much proof and understanding of an initial singularity as we do of God. Let's focus on those things that can conceivably be observed in the near future.

Actually, I wasn't arguing against time being infinite. I was only arguing against space being infinite because it would either take an infinite time to get that big or it would have to be created all in an instant. In either case any understanding of how things evolved would be lost in a infinite progression into the past.

I do make an exception: that the universe started in the infinite past at an infinitesimal size. If the exponential expansion of inflation is true, then exponentials decrease to zero only in the infinite past. With no, or very little structure presumed at the infinitesimally small, cause and effect is not lost in instant complexity.

 

[Mike2]

Expansion / inflation does not require a finite, or infinite universe. It also has nothing to do with the finite speed of light. The finite speed of light only constrains how much of the universe is visible to us at any given time after the Big Bang. And, as an added bonus, you can become greatly confused just thinking about that! [SpaceTiger has patiently tried, and I much appreciate his efforts to elevate my understanding on that point.]

Of course, that assumes there was a Big Bang. But you don't need a BB event to arrive at the same conclusion. Most cosmologists favor the BB model because it's the one that agrees with the preponderance of evidence.

I think inflation necessitates a finite universe. For it is assumed to grow, presuming that it was originally small, and has not grown to infinity yet.

Some things about inflation confuse me. The universe is supposed to be much bigger than our present cosmological event horizon will allow us to see. (60 e-folds bigger, as I have read somewhere, whatever e-folds are). But we can presumably see back to the time when atom first formed and light could travel without hinderance, the CMBR. How big was the universe at the time of last scattering? Are we seeing all of the surface of last scattering, or just part of it? Are there other places in the universe where last scattering occurred but we will never see because it is beyond our cosmological event horizon?

 

[Chronos]

An infinite universe has maddening paradoxes in plain view.

 

[SpaceTiger]

Actually, I wasn't arguing against time being infinite. I was only arguing against space being infinite because it would either take an infinite time to get that big or it would have to be created all in an instant.

I know what you were suggesting. I'm telling you that your claim is incorrect. If you're talking about the observable universe, then you're right, it would take an infinite time to become infinite in size, but spacetime itself is under no such restriction. The big bang is not an explosion in a pre-existing space, so it does not have to be causally connected in our spacetime.

I don't really believe that the universe will end up being spatially infinite, but you can't rule it out with observations at this point.

If the exponential expansion of inflation is true, then exponentials decrease to zero only in the infinite past.

Traditional theories of inflation give it both a beginning and an end. The typical number of e-foldings in a theory describing the last inflationary period is around 50-100.

 

[SpaceTiger]

Anyway, I've got a question. Somewhere in my
brief readings and musings about things cosmological
I've gotten the idea that the rate of expansion should be
connected somehow to the speed of light in a
vacuum.

Is there anything to this in the standard
cosmological model(s)?

In traditional cosmology, there is no connection between the expansion rate and the speed of light. Very distant galaxies will recede from us at greater than the speed of light and closer ones will recede more slowly. The boundary at which v_r=c (relative to us) is of little physical consequence.

 

[SpaceTiger]

How big was the universe at the time of last scattering?

There are several ways to answer this question. If you mean the size of the observable universe, then the best way to estimate is to look at the first peak in the power spectrum of the CMB. That gives the approximate comoving horizon size at decoupling (another name for the last scattering era). It's at angular scales of ~1 degree, which corresponds to a comoving size ~300 times smaller than our observable universe.

Another way to answer it is to give the relative physical scale for the currently observable universe. This is given by the redshift of decoupling, which is ~1000. This means that the parts of the universe that are currently observable were contained in a volume 1000 times smaller at the time of decoupling.

Yet another way is to give the relative physical size of the horizon at decoupling to the horizon at present. To get this, you just multiply the above two numbers together and find that the horizon was 300,000 times smaller.

Finally, if you're asking about the physical size of the entire surface of last scattering, including the stuff we can't see, then nobody knows. Current models indicate that the universe is almost perfectly flat, so the surface of last scattering is likely much bigger than we can currently observe.

Are there other places in the universe where last scattering occurred but we will never see because it is beyond our cosmological event horizon?

If the next epoch of exponential expansion is permanent, then yes. If not, it's hard to say.

 

[Sherlock]

In traditional cosmology, there is no connection between the expansion rate and the speed of light. Very distant galaxies will recede from us at greater than the speed of light and closer ones will recede more slowly.

Ok, that's what I'd expect to find.

The boundary at which v_r=c (relative to us) is of little physical consequence.

Could one think of the speed of light as being a maximum
at/near the universal boundary and then dropping off
in some proportion as the distance from the boundary
increases. Sort of related to the 'stretching' of 'space'
due to expansion, which I would expect to maximize at the
boundary where expansion rate is largest (the
boundary being defined as the universal 'wave front'), and
then decrease as the distance from the boundary increases?

 

[SpaceTiger]

Could one think of the speed of light as being a maximum
at/near the universal boundary and then dropping off
in some proportion as the distance from the boundary
increases. Sort of related to the 'stretching' of 'space'
due to expansion, which I would expect to maximize at the
boundary where expansion rate is largest (the
boundary being defined as the universal 'wave front'), and
then decrease as the distance from the boundary increases?

I'm not quite sure what you mean. The recession speed of galaxies increases with distance from the earth, eventually going well beyond the speed of light. There is a distance at which galaxies are receding at approximately the speed of light, but this distance is not important. If we were viewing the universe from another galaxy, the "sphere" inside which galaxies were receding at less than the speed of light would be different.

As for the expansion rate (parameterized by the Hubble constant), that's usually assumed to be independent of position, by the cosmological principle. The recession velocity of galaxies relative to us is not a measure of the expansion rate because it depends on distance. To first order:

$$v_r=H_0d$$

where H₀ is hubble's constant and d is the distance from us.

 

[Mike2]

I know what you were suggesting. I'm telling you that your claim is incorrect. If you're talking about the observable universe, then you're right, it would take an infinite time to become infinite in size, but spacetime itself is under no such restriction. The big bang is not an explosion in a pre-existing space, so it does not have to be causally connected in our spacetime.

I'm not necessarily talking about causality in terms of the speed of light. I'm talking about causality in terms of one thing happening as the basis of events some time after that. Yes, inflation is supposed to have space expanding very very fast, so that most places are receding from other places faster than light. Still it was at some speed so that it is at least theoretically possible to trace the sequence of events that lead to the present condition. But if the universe were infinite in extent, then it would take an eternity to get there so that it would no longer be possible to trace the sequence of events that lead to it and we could not even in theory know what is the cuase of it all. Or the infinite universe was created instantaneously which again negates any possibility of tracing the sequence of events so that no theory of creation could ever possibly be proven.

Traditional theories of inflation give it both a beginning and an end. The typical number of e-foldings in a theory describing the last inflationary period is around 50-100.

Obviously I'm asking what the term "e-fold" is? Thank you.

 

[Sherlock]

I'm not quite sure what you mean.

I'm not either. :-) Cosmology is fascinating. I once
read a book called Frozen Star (or something like that), and
have picked up bits and pieces here and there. However,
I have only a very pedestrian, very naive apprehension of
the field. For example, I don't know what it means to say
(that is, how it's calculated) that some galaxies are moving
away from us at superluminal speeds.

Anyway, thanks (and to others too) for replying.

What's a good intro to the nuts and bolts of cosmological
model-making? Not too advanced, but I'm ok with algebra,
linear algebra, calculus, the usual intermediate stuff.
So, something along the lines of a more conceptual
intro -- but not just a popularization of it.

I haven't gotten around to reading all the journals
of the advisors and mentors here yet. This hasn't been
my main area of interest, but I can see how one could
get hooked on cosmology.

The recession speed of galaxies increases with distance from the earth, eventually going well beyond the speed of light. There is a distance at which galaxies are receding at approximately the speed of light, but this distance is not important. If we were viewing the universe from another galaxy, the "sphere" inside which galaxies were receding at less than the speed of light would be different.

As for the expansion rate (parameterized by the Hubble constant), that's usually assumed to be independent of position, by the cosmological principle. The recession velocity of galaxies relative to us is not a measure of the expansion rate because it depends on distance. To first order:

$$v_r=H_0d$$

where H₀ is hubble's constant and d is the distance from us.

That the recession velocity increases with distance was
part of my consideration. I assumed that the isotropic expansion
rate also increases with distance from us, and that the speed of
light in vacuum also increases with distance from us. Then,
assuming a finite, bounded universe, the expansion rate (and the
speed of light) would reach a maximum at the boundary. And,
then I wondered if the (finite) expansion rate could be related
to the finite propagational rates of all the phenomena that
we're familiar with, including light -- in some limiting sense.
Which all had to do with *first* wondering about whether it
would be possible for an object inside our universe to
accelerate beyond the boundary, and also about what
the physical basis for inertia might be.

As you can see, this is a bit ... scattered. I think I really
need that intro. :-)

 

[SpaceTiger]

I'm not necessarily talking about causality in terms of the speed of light. I'm talking about causality in terms of one thing happening as the basis of events some time after that.

Yes, but how does one apply those principles to the beginning of time? What came first, the cause or the effect? Again, I don't think it matters what speed you give to causality, it still doesn't make sense to apply these arguments to the initial singularity. The creation of spacetime itself is not an event within spacetime, so we can't say anything about what limits it.

Obviously I'm asking what the term "e-fold" is? Thank you.

My apologies, I overlooked that part of your post. An "e-fold" is just an increase in the scale factor (physical scale) of the universe by a factor of e.

 

[SpaceTiger]

What's a good intro to the nuts and bolts of cosmological
model-making? Not too advanced, but I'm ok with algebra,
linear algebra, calculus, the usual intermediate stuff.
So, something along the lines of a more conceptual
intro -- but not just a popularization of it.

Well, unfortunately, I think there's a paucity of good textbooks at that level, but I can recommend the following:

 

[Simetra7]

The recession speed of galaxies increases with distance from the earth, eventually going well beyond the speed of light. There is a distance at which galaxies are receding at approximately the speed of light, but this distance is not important. If we were viewing the universe from another galaxy, the "sphere" inside which galaxies were receding at less than the speed of light would be different.

I'm having some trouble understanding the exact meaning of the recession speed of galaxies. It has been stated in earlier posts in this thread that these galaxies are not actually speeding away from us but rather the space between us and them is expanding. Does this mean that the galaxies themselves are in effect "at rest", while space stretches out all around them, and if so is the recession speed only a perceived observation which depends entirely on the distance the galaxy is viewed from? What i am trying to say is, how can something be at rest, and have a velocity at the same time?

 

[SpaceTiger]

I'm having some trouble understanding the exact meaning of the recession speed of galaxies. It has been stated in earlier posts in this thread that these galaxies are not actually speeding away from us but rather the space between us and them is expanding.

You're correct, I'm being sloppy with my terminology. The physical distance between us and them is increasing, but this isn't due to motion in space, but rather the expansion of space itself.

Does this mean that the galaxies themselves are in effect "at rest"

On average, yes, though they do usually have an extra velocity due to influences from nearby objects.

What i am trying to say is, how can something be at rest, and have a velocity at the same time?

Objects move through space according to the rules set down in general relativity, but those rules do not apply to the space(time) itself. Remember that this "motion" that they appear to have from our point of view is only a consequence of where we're viewing them from. If we were on another galaxy, they'd appear to be moving in a different direction.

 

[Mike2]

Yes, but how does one apply those principles to the beginning of time? What came first, the cause or the effect? Again, I don't think it matters what speed you give to causality, it still doesn't make sense to apply these arguments to the initial singularity. The creation of spacetime itself is not an event within spacetime, so we can't say anything about what limits it.

I think we are in agreement here. You say "beginning of spacetime". And we talk about "expansion". So doesn't that in and of itself imply that the universe cannot be infinite - that expansion would take forever to get to infinity?

My apologies, I overlooked that part of your post. An "e-fold" is just an increase in the scale factor (physical scale) of the universe by a factor of e.

So 60 e-folds is a scale factor of e^60?

 

[SpaceTiger]

I think we are in agreement here. You say "beginning of spacetime".

No, I said "creation of spacetime". The distinction is important because "beginning" implies some sequential set of events, and those only happen within spacetime. Spacetime itself just is.

And we talk about "expansion". So doesn't that in and of itself imply that the universe cannot be infinite - that expansion would take forever to get to infinity?

It may be that an infinite universe can expand infinitely, remaining infinite all along. The point is that we just don't know. Scientists avoid infinities because they're difficult to deal with and because, historically, they've indicated problems in a theory. However, that doesn't mean they can't occur. A good scientist should be careful not to impose any such preconceived notions upon the universe. We've learned this lesson many times in the past.

So 60 e-folds is a scale factor of e^60?

That's right.

 

[davstar]

expansion on the local scale

The expansion of the universe is indeed a difficult concept to explain without resort to mathematics. Assuming for the moment that the expansion of spacetime is a fact then the bodies in the solar system are also receding from each other. I've seen arguments by professionals that this does not apply to the local scale because the gravitational forces acting between the bodies do not allow this, but this cannot be relevant if space itself is expanding. I wonder if it would be possible to measure this expansion within the solar system e.g. by measuring signals between the Earth and orbiting satellites. Perhaps the effect is too small for modern techniques to measure. It would certainly provide undeniable proof whether expansion is occurring or not.

 

[SpaceTiger]

I've seen arguments by professionals that this does not apply to the local scale because the gravitational forces acting between the bodies do not allow this, but this cannot be relevant if space itself is expanding.

It's not that it's not "allowed", it's that the local forces dominate the changes in displacement. In that case, the physical separation between two objects changes more from their movement through spacetime than from the expansion of spacetime itself.

I wonder if it would be possible to measure this expansion within the solar system e.g. by measuring signals between the Earth and orbiting satellites. Perhaps the effect is too small for modern techniques to measure.

It is indeed.

 

[Mike2]

No, I said "creation of spacetime". The distinction is important because "beginning" implies some sequential set of events, and those only happen within spacetime. Spacetime itself just is.

Even from within spacetime there is a sense of a beginning in terms of the structure within. It would seem that complicated structures would have to come from the more simplistic. But if complicated structure should arise instantaneously, then all hope of tracing the sequence of events is lost. Or if complicated structure continues forever in all direction, then again all hope of tracing the sequence of events that lead to it is lost. So we must have a finite universe if there is any hope of obtaining a TOE.

 

[turbo]

Even from within spacetime there is a sense of a beginning in terms of the structure within. It would seem that complicated structures would have to come from the more simplistic. But if complicated structure should arise instantaneously, then all hope of tracing the sequence of events is lost. Or if complicated structure continues forever in all direction, then again all hope of tracing the sequence of events that lead to it is lost. So we must have a finite universe if there is any hope of obtaining a TOE.

Imagine that the Universe had NO beginning and that it is infinite in spatial extent and time. What does this do to your insistence on causality? I would think that your insistence on causality would give you a lot of trouble if you adhere to a BB model, especially a finite one. Infinite steady-state cosmologies can easily accommodate a TOE.

 

[SpaceTiger]

Even from within spacetime there is a sense of a beginning in terms of the structure within. It would seem that complicated structures would have to come from the more simplistic. But if complicated structure should arise instantaneously, then all hope of tracing the sequence of events is lost. Or if complicated structure continues forever in all direction, then again all hope of tracing the sequence of events that lead to it is lost.

I'm not sure how complexity enters into this. The discussion is about the beginning of time and whether it can begin as spatially infinite in extent. The initial conditions of the universe can be arbitrarily simple and yet still infinite in extent. In fact, some might argue that an infinite universe is simpler than one with an arbitrary scale.

 

[Mike2]

Imagine that the Universe had NO beginning and that it is infinite in spatial extent and time. What does this do to your insistence on causality? I would think that your insistence on causality would give you a lot of trouble if you adhere to a BB model, especially a finite one. Infinite steady-state cosmologies can easily accommodate a TOE.

How could you explain where spacetime itself came from if it were eternally existing and/or infinite in extent? Such a premise is a direct denial of any explanation. Such a position is the same as saying, "There is no explanation; it just instantaneously popped into existence." Or it would be the same as saying, "There is no explanation for where it came from because it has always been here." If the universe as a whole defies explanation, then why should you think any part of it could be explained?

 

[Chronos]

How could you explain where spacetime itself came from if it were eternally existing and/or infinite in extent? Such a premise is a direct denial of any explanation. Such a position is the same as saying, "There is no explanation; it just instantaneously popped into existence." Or it would be the same as saying, "There is no explanation for where it came from because it has always been here." If the universe as a whole defies explanation, then why should you think any part of it could be explained?

You are correct, IMO, in questioning both arguments. It is just as confounding to propose a universe from nothing as it is to propose a universe that always was.

Observational evidence indicates, but does not prove, our universe is temporally finite - just that the preponderance of evidence supports this conjecture. I allow, however, this may merely reflect the limits of our ability to perceive and describe our observable evidence.

 

[turbo]

How could you explain where spacetime itself came from if it were eternally existing and/or infinite in extent?

If the Universe is infinite in all space and time, it simply exists, and asking for a creation story (Where did it come from?) is futile.

Such a premise is a direct denial of any explanation. Such a position is the same as saying, "There is no explanation; it just instantaneously popped into existence."

There is a not-so-subtle point that you are missing - a spacially and temporally infinite universe simply IS. It does not exist relative to anything else, nor can you consider that it "popped into esistence".

Or it would be the same as saying, "There is no explanation for where it came from because it has always been here."

That's a whole lot closer to the truth.

If the universe as a whole defies explanation, then why should you think any part of it could be explained?

We can certainly explain large parts of the Universe, although our models do not agree on some scales (thus the problems encountered in developing a theory of quantum gravity). This indicates that one or more of our models need to be modified or supplanted.

Like Space Tiger said above "some might argue that an infinite Universe is simpler than one with an arbitrary scale". I would take that position. As for the need to define the entire Universe relative to something else in hopes of satisfying causality, that is a losing battle. You then need to define the properties if the background against which the Universe "popped into existence" and explain why that background existed in the first place, and then you'll need a "creation story" to establish causality regarding the origin of that background, and so forth in infinite regression. It may not sound logical to you, but it is easier to contemplate the existence of a spacially and temporally infinite universe, than to play the causality game ad infinitum.

 

[SpaceTiger]

How could you explain where spacetime itself came from if it were eternally existing and/or infinite in extent?

I think you're taking "Theory of Everything" too literally. There will always be something whose origin cannot be explained. With traditional cause and effect, every cause must have its own cause, so an infinite chain is the only way out of an unexplainable beginning.

This discussion has long since left the realm of science, so perhaps you should bring up the issue in one of the philosophy forums.

 

[hellfire]

I just cannot imagine how physics can make a strict sense of any kind of infinite value. In this case an infinite amount of time from an infinite past. This would need of an infinite number of events to reach present. Does this make sense? Is present actually possible in such a model? It remembers me to the paradoxes related to the spatial infinite. For example, can a force (e.g. gravity) be acting on a body located at an infinite distance? This body will never change its position as it will always stay at infinity (oo - N = oo). It seams that the concept of position makes no sense at infinity. I have a bad feeling with this, and I think something similar goes on with an infinite past. I would be more happy with the existence of a state which is uncaused and from which the causal chain and time arise (may be as some fluctuation or break of symmetry).

 

[Simetra7]

Remember that this "motion" that they appear to have from our point of view is only a consequence of where we're viewing them from. If we were on another galaxy, they'd appear to be moving in a different direction.

Is there a distinct point (distance from Earth in every direction), where this apparent motion starts to become observable, or is the observed expansion rate very different at a particular distance in one direction than it is at the same distance in another direction?

 

[SpaceTiger]

Is there a distinct point (distance from Earth in every direction), where this apparent motion starts to become observable, or is the observed expansion rate very different at a particular distance in one direction than it is at the same distance in another direction?

It depends on the magnitude of the local motions, but it will be roughly the same no matter what direction you look. Basically, you'll see the effects of expansion when,

$$H_0d \sim v_{gal}$$

The magnitude of the galaxy's peculiar velocity (v_gal) will depend on where it's located, but on average, does not depend on direction. As for H₀, it certainly doesn't depend on direction.

 

[Simetra7]

Does the expansion of space effectively give us an almost static view of distant objects in space? For example, the furthest observable galaxy in the Hubble deep field has been estimated to be approximately 13 billion light years away, so the light that is observed from that galaxy is from 13 billion years ago, when the universe was only an estimated 1 billion years old. At that time, the position that Earth now occupies in space would have been much closer to that particular galaxy, so an observer, (had there been anyone around at that time to observe), would have seen that galaxy at almost the same period in it's evolution as we are seeing it now. So in 14 billion years, only 1 billion years worth of the evolution of that galaxy has been observable, but it has been stretched out over the whole of those 14 billion years. Does this make any sense?

 

[Garth]

It depends on the magnitude of the local motions, but it will be roughly the same no matter what direction you look. Basically, you'll see the effects of expansion when,

$$H_0d \sim v_{gal}$$

The magnitude of the galaxy's peculiar velocity (v_gal) will depend on where it's located, but on average, does not depend on direction. As for H₀, it certainly doesn't depend on direction.

When the Earth's velocity around the Sun has been taken into account the Solar System is traveling at 390 +/- 60 km/sec relative to the surface of last emission of the CMB. However when the Sun's motion around the Galaxy is also taken into account this translates into the fact that the Galaxy is traveling relative to the surface of last emission of the CMB, which probably defines the C.M. reference frame of the universe, at 603 km/sec or about 0.2%c! (Nature, Vol 270, 3 Nov 1977, pg 9) Therefore, if our galaxy's velocity is 'typical', then
$$H_0d \sim 0.002c$$ or d ~ 10 Mpsc

So in 14 billion years, only 1 billion years worth of the evolution of that galaxy has been observable, but it has been stretched out over the whole of those 14 billion years. Does this make any sense?

Yes, you are describing cosmological time dilation, otherwise detected as cosmological red shift.

Garth

 

[Chronos]

I usually avoid these conversations. You are not seeing the 'big picture' here, Simretra7. You are making unfounded assumptions about the initial state of the universe and extrapolating them way beyond what is reasonable. It makes no sense.

 

[Simetra7]

I usually avoid these conversations. You are not seeing the 'big picture' here, Simretra7. You are making unfounded assumptions about the initial state of the universe and extrapolating them way beyond what is reasonable. It makes no sense.

My intention was not to make any sort of an assumption but just to try to make sense out of what is a fascinating but extremely complicated subject.
Are you saying that our view of far off objects is not a "slow motion" view, or is it just my reasoning that is unreasonable.

 

[hellfire]

Does the expansion of space effectively give us an almost static view of distant objects in space? For example, the furthest observable galaxy in the Hubble deep field has been estimated to be approximately 13 billion light years away, so the light that is observed from that galaxy is from 13 billion years ago, when the universe was only an estimated 1 billion years old. At that time, the position that Earth now occupies in space would have been much closer to that particular galaxy, so an observer, (had there been anyone around at that time to observe), would have seen that galaxy at almost the same period in it's evolution as we are seeing it now. So in 14 billion years, only 1 billion years worth of the evolution of that galaxy has been observable, but it has been stretched out over the whole of those 14 billion years. Does this make any sense?

Yes, this makes sense. Further on, objects located very near to our spatial position at an instant of time after t = 0 would have been observable to an observer located at our spatial position, but after 13.7 Gyr we would see them now exactly in the same instant of their evolution as this observer did.

This is due to the fact that in a dynamic space with an initial singularity the past light cone is not a cone but a "teardrop". In a static space, the size of the particle horizon now is the same as the size of the past light cone at t = 0. For a dynamic space this is not true, since the size of the light cone is zero at t = 0.

The term particle horizon refers to the current location of the objects which sent us a light ray at t = 0 that we are observing now. The term past light cone refers to the objects located in past which have a causal influence on us.

May be figure 1 in http://arxiv.org/astro-ph/0310808 will help.

 

[Simetra7]

May be figure 1 in http://arxiv.org/astro-ph/0310808 will help.

Could you check this link. I think it may be the wrong one.

 

[hellfire]

The link is correct. Go to Full-Text: PDF, and open the document ("Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe"). You may take a look to Figure 1 and try to understand what happens with the light cone and the particle horizon. If you have questions, please ask.