I Simply Cannot Understand Olbers' Paradox -- Finite/Infinite Universe

[BHL 20]

My astrophysics lecturer did Olbers' paradox today in class, and while discussing it, it seemed as if she actually believes that the universe is infinite (infinite amount of space and infinite amount of matter). I came and questioned her about this afterwards, and when I said I had always thought that a finite amount of matter was produced in the Big Bang, she just replied "I'm not sure you're right about that" in a voice that suggested she thought I was flat out wrong.

As far as I can see there are two scenarios which would lead to an infinite amount of matter being present in the universe:
1) An infinite amount of matter was created in a process which took a finite time.
2) A matter-creating process has been active for an infinite amount of time.

(2) requires an eternal universe and therefore contradicts what we know about the Big Bang. It's reminiscent of the theories espoused by Fred Hoyle and his colleagues in the mid-20th century. (1) is so mind-blowing that if a theory of such a process existed, or even if there was reasonable speculation that such a process had occurred, it would talked about everywhere in pop science, some lecturer or other would have at least mentioned it, and it would form the basis for a revolution in science of similar magnitude to the discovery of relativity or quantum mechanics. In other words I would know about it already.

Am I missing anything?

 

[PeterDonis]

when I said I had always thought that a finite amount of matter was produced in the Big Bang, she just replied "I'm not sure you're right about that" in a voice that suggested she thought I was flat out wrong.

Our best current model of the universe does, in fact, say that the universe is infinite and contains an infinite amount of matter. It also does not say that the matter in the universe was "produced" in the Big Bang, except in the trivial (for this purpose) sense that the matter and energy we currently observe did not always exist in the same form. Our current model of the universe only goes back to the inflationary epoch; it does not make any claim about what happened before the inflationary epoch, or how inflation was started. The term "Big Bang", properly used, does not refer to an "initial singularity" where everything in the universe was created (although pop science presentations often make this mistaken claim); it only refers to the fact that, at the end of inflation, the universe was in a very hot, dense state and was expanding very rapidly.

As far as I can see there are two scenarios which would lead to an infinite amount of matter being present in the universe:

You left out two more:

3) An infinite amount of matter/energy has always existed.

4) The universe actually contains zero net matter/energy; the positive contribution of the ordinary matter and energy we see is canceled out by a negative contribution from something else, making the total zero.

There isn't really a consensus among cosmologists about which of #3 or #4 is correct, but AFAIK pretty much everyone thinks it's one of the two.

 

[Chalnoth]

There are also entirely-finite models of the universe, in addition to infinite models. The fact is that nobody knows, and due to quantum mechanics the question may actually not be relevant: in an infinite universe, there are infinite exact copies of every observable universe that exists. But isn't this just multiple-counting? If observable universe A and observable universe B are exact copies of one another, and have histories and futures that are identical, then doesn't it make sense to not count the copies as separate entities?

If we don't count more than one copy of any possible observable universe, then quantum mechanics suggests that there are a finite (though large) number of possible observable universes, which provides an upper limit to the total unique volume.

 

[BHL 20]

But I've read many assertions about the size of the early universe such as "after inflation the universe was the size of a grapefruit". This paper http://arxiv.org/PS_cache/astro-ph/pdf/0305/0305179v1.pdf even graphs the size of the universe against time on page 30. How can an infinite amount of matter be contained in a finite volume?

 

[Chalnoth]

But I've read many assertions about the size of the early universe such as "after inflation the universe was the size of a grapefruit". This paper http://arxiv.org/PS_cache/astro-ph/pdf/0305/0305179v1.pdf even graphs the size of the universe against time on page 30. How can an infinite amount of matter be contained in a finite volume?

They're talking about the region that became our observable universe.

 

[BHL 20]

They're talking about the region that became our observable universe.

If you're correct, that's very deceptive.

 

[Chalnoth]

If you're correct, that's very deceptive.

Yes. It's really unfortunate that most of the time when the word "universe" is used, they actually mean, "observable universe". And then sometimes the same person will switch to using the word "universe" to mean more than just the observable universe. It's just really bad language.

When you throw the word "multiverse" in, the language can become even more convoluted. Universe technically means "all that exists", so if one is to take that meaning seriously, "multiverse" should just be a synonym for "universe". To make things even worse, people mean very different things by the word "multiverse". Yes, it's all confusing. And it's really not much better within the scientific community either. Not a very good state of affairs in general.

 

[marcus]

But I've read many assertions about the size of the early universe such as "after inflation the universe was the size of a grapefruit". This paper http://arxiv.org/PS_cache/astro-ph/pdf/0305/0305179v1.pdf even graphs the size of the universe against time on page 30. How can an infinite amount of matter be contained in a finite volume?

http://arxiv.org/abs/astro-ph/0305/0305179
On page 30 Lineweaver's graph is labeled "the size of the universe in units of its present size". What that means is the size of a generic distance compared to its present size (set equal to 1). That number, which Lineweaver denotes R(t), is called the "scale factor".
The scale factor (which he plots over time on page 30) is defined in a spatially infinite universe with infinite matter in exactly the same way as in a finite universe.
Think of it as "the scale of the universe" rather than an overall size. The universe may have no definite overall size since it might be infinite and in any case we do not know the overall size so we can't talk about it.

But we can track the growth of a generic distance, and plot that, and normalize it so the present size is ONE. So R(t_present) = 1
And if we see a galaxy whose light is coming in wavelengths stretched by a factor of 3, we call that redshift z = 2, and R(t_z=3) = 1/3
We see that galaxy as it was back when distances were 1/3 present size, so while the light was traveling to us distances were enlarged by a factor of 3 and wavelengths enlarged along with them. The scale factor, or distance size factor if you want to call it that, is related in a simple way to redshift z. It is 1/(z+1).

Sorry Lineweaver's language confused you! He was NOT talking about the "size of the observable universe". His plot on page 30 does not show the size of the observable universe, which has grown on a different schedule from the scale factor. Check out Lineweaver Figure 1 in that paper, look at the PARTICLE HORIZON curve. That shows the growing extent of the observable region. Lineweaver was not talking about the "grapefruit" you hear about in popularizations.

They're talking about the region that became our observable universe.

If you're correct, that's very deceptive.

I agree that talking about "grapefruit after inflation" can be very misleading. Even if you specify "observable" grapefruit! :) Talk like that is speculative and needs to be strongly qualified. A lot of current research concerns BOUNCE models some of which do not require inflation in order to reproduce observed cosmological results. Inflation has problems. There was a panel discussion about this at the December Paris conference where they discussed the implications of the most recent set of Planck mission data. Steinhardt Mukhanov Brandenberger and Linde were the panel. Interesting discussion. Also I think this paper is a good representative of growing research interest, you might have a look.
http://arxiv.org/abs/1412.2914
A ΛCDM bounce scenario
Yi-Fu Cai, Edward Wilson-Ewing
(Submitted on 9 Dec 2014)
We study a contracting universe composed of cold dark matter and radiation, and with a positive cosmological constant. As is well known from standard cosmological perturbation theory, under the assumption of initial quantum vacuum fluctuations the Fourier modes of the comoving curvature perturbation that exit the (sound) Hubble radius in such a contracting universe at a time of matter-domination will be nearly scale-invariant. Furthermore, the modes that exit the (sound) Hubble radius when the effective equation of state is slightly negative due to the cosmological constant will have a slight red tilt, in agreement with observations. We assume that loop quantum cosmology captures the correct high-curvature dynamics of the space-time, and this ensures that the big-bang singularity is resolved and is replaced by a bounce. We calculate the evolution of the perturbations through the bounce and find that they remain nearly scale-invariant. We also show that the amplitude of the scalar perturbations in this cosmology depends on a combination of the sound speed of cold dark matter, the Hubble rate in the contracting branch at the time of equality of the energy densities of cold dark matter and radiation, and the curvature scale that the loop quantum cosmology bounce occurs at. Finally, for a small sound speed of cold dark matter, this scenario predicts a small tensor-to-scalar ratio.
14 pages, 8 figures
LambdaCDM is the standard cosmic model. They simply started it off with a rebound from prior contracting phase, and found they can omit inflation (which is inserted in many other models to produce effects like homogeneity which Cai and Wilson-Ewing get without inflation.

Cai is a close collaborator with Brandenberger who is on this panel
http://webcast.in2p3.fr/videos-debate_theoretical_problems_way_forward
As introduction to the debate, to get things started, Steinhardt gave a critical review:
http://webcast.in2p3.fr/videos-introduction-_critical_review_of_inflation

 

[BHL 20]

One more thing, but this is probably a big thing. I'm shocked by this:

The term "Big Bang", properly used, does not refer to an "initial singularity" where everything in the universe was created (although pop science presentations often make this mistaken claim); it only refers to the fact that, at the end of inflation, the universe was in a very hot, dense state and was expanding very rapidly.

No singularity? I know Wikipedia isn't the most reliable but a lot of people get their information from it, and in the introduction to the article in it on the Big Bang it says that it "postulates that at some moment all of space was contained in a single point from which the universe has been expanding ever since." What about all the speculation about what came before the Big Bang and the Hartle-Hawking no-boundary proposal? You guys sound as you're from a different planet.

 

[Chalnoth]

One more thing, but this is probably a big thing. I'm shocked by this:
No singularity? I know Wikipedia isn't the most reliable but a lot of people get their information from it, and in the introduction to the article in it on the Big Bang it says that it "postulates that at some moment all of space was contained in a single point from which the universe has been expanding ever since." What about all the speculation about what came before the Big Bang and the Hartle-Hawking no-boundary proposal? You guys sound as you're from a different planet.

Many popularizations of the big bang theory contain this misleading piece.

First, it is absolutely correct that the classic Big Bang theory, which takes the current contents of the universe and extrapolates back in time, has a singularity. But we cannot take that singularity seriously: in essence, it is a division by zero. Such a division by zero is mathematical gibberish. Because it is gibberish, it is not possible for it to describe anything about reality.

The reason why so many popularizations focus on this singularity, I think, is that people really like narratives. They like to describe the universe as, "There was this, and then this happened which made that, etc." But this is disingenuous and inaccurate. A better way of understanding the universe is to think of it in terms of how clearly we can see. We can see the recent history of the universe quite clearly. As we extrapolate back in time, things get more and more uncertain, because our vision is no longer up to the task of seeing that far back, for essentially the same reason that it's hard to read small text at a large distance. So the better way of describing our universe is as a reverse narrative: currently we live in an expanding universe that is getting cooler. As we look into the past, things were closer together and the universe was warmer. As our universe gets denser and denser further into the past, we can make various predictions about the sorts of matter that should have been around. As long as we don't follow the thread all the way back to where the theory becomes nonsensical, we get pretty good predictions.

 

[phinds]

No singularity?

To slightly restate what Chalnoth said, part of the problem is that in science, "singularity" does NOT mean "point in space" in means "the place where the model breaks down and gives a conclusion that cannot be physical reality". In pop-sci, it is interpreted (completely incorrectly) to mean "point in space".

 

[BHL 20]

Thank you everyone for the replies. So I guess this means that if we improve our theories, we may eventually be able to get rid of the singularity. Interesting.

 

[Chronos]

Many singularities in physics were resolved by a mathematical technique known as renormalization. The mathematics of gravity are such they have far resisted all attempts at renormalization thus far. That is why quantum gravity is such a hot topic in physics. The quantum version of gravity should be renormalizable allowing us to resolve gravitational singularities.

 

[marcus]

Thank you everyone for the replies. So I guess this means that if we improve our theories, we may eventually be able to get rid of the singularity. Interesting.

That's right. Various modifications or improvements of standard LCDM cosmology have been proposed that eliminate the singularity.
My impression is that the type of proposal that's popular now, for researchers to work on, if you just look at professional work published in the past 3 or 4 years, is the bounce type of modification.
An example of that is the December 2014 paper by Cai and Wilson-Ewing that I reference in post #8. In that, standard LCDM cosmology expansion starts as a rebound from collapsing phase of the same universe, with same matter/physical laws. You do not get a breakdown of theory (i.e. "singularity"), you do not get infinities, you do not need inflation, you do not need to assume an imagined "inflaton" particle. You get results consistent with observation, as far as their analysis goes. They still have more to do, and more details to check (which they describe at the end of the paper).
If you want to read it, the link is in post#8. Or here:
http://arxiv.org/pdf/1412.2914v1.pdf
It is an example of the type of thing a number of researchers are studying currently, in different versions and variations.

You say "if" we improve our theories we "may" get rid of the singularity. (i.e. the breakdown failure of classical LCDM right at the start of expansion).
I feel fairly confident that cosmologists WILL improve the classical LCDM model and WILL replace it with a model that does not suffer that technical failure.
People like Cai and Wilson will propose something, work out the details, make predictions about new observations, which will check out, and the community consensus will gradually shift over to a "singularity-free" model.

Other people may disagree and may not feel as confident about that as I do. But I follow the quantum cosmology research literature fairly closely and that is the PoV that I've come around to. It isn't decided yet, but we'll see. :w

 

[Chalnoth]

That's right. Various modifications or improvements of standard LCDM cosmology have been proposed that eliminate the singularity.
My impression is that the type of proposal that's popular now, for researchers to work on, if you just look at professional work published in the past 3 or 4 years, is the bounce type of modification.
An example of that is the December 2014 paper by Cai and Wilson-Ewing that I reference in post #8. In that, standard LCDM cosmology expansion starts as a rebound from collapsing phase of the same universe, with same matter/physical laws. You do not get a breakdown of theory (i.e. "singularity"), you do not get infinities, you do not need inflation, you do not need to assume an imagined "inflaton" particle. You get results consistent with observation, as far as their analysis goes. They still have more to do, and more details to check (which they describe at the end of the paper).
If you want to read it, the link is in post#8. Or here:
http://arxiv.org/pdf/1412.2914v1.pdf
It is an example of the type of thing a number of researchers are studying currently, in different versions and variations.

You say "if" we improve our theories we "may" get rid of the singularity. (i.e. the breakdown failure of classical LCDM right at the start of expansion).
I feel fairly confident that cosmologists WILL improve the classical LCDM model and WILL replace it with a model that does not suffer that technical failure.
People like Cai and Wilson will propose something, work out the details, make predictions about new observations, which will check out, and the community consensus will gradually shift over to a "singularity-free" model.

Other people may disagree and may not feel as confident about that as I do. But I follow the quantum cosmology research literature fairly closely and that is the PoV that I've come around to. It isn't decided yet, but we'll see. :w

It's a bit disingenuous to claim that you need nothing more than LCDM to get this result. You do need something more: you need to use loop quantum gravity as your model for quantum gravity. Loop quantum gravity is still fairly speculative.

Cosmic inflation, on the other hand, makes use of effective field theory, which is highly independent of the specific physics at high energies.

Whether adding a new particle or an entire proposed theory is more speculative is a matter of opinion.

 

[PeterDonis]

you do not need inflation, you do not need to assume an imagined "inflaton" particle

But don't you effectively need something like it to create the bounce? That is, don't you need something with the same sort of equation of state at the classical level as an "inflaton" (and a very different equation of state from ordinary matter or radiation) to create the bounce? If so, then it seems like the bounce cosmology is really just an extension of the current LCDM/inflation cosmology.

 

[marcus]

You do need something more: ...

That's right! You need something more and that is precisely my point!
Brandenberger's group at McGill has been studying "matter bounce" rebound. Odintsov's group at Barcelona has a variant involving teleparallel or modified gravity (look at Jaume deHaro's papers). There are a number of other versions of the idea.

you need to use loop quantum gravity as your model for quantum gravity. ...

No you certainly do not need LQG! The bounce cosmology idea includes a number of different concepts. It has gotten popular with researchers and they take different approaches.

It's a bit disingenuous to claim that you need nothing more than LCDM to get this result. ...

I claimed nothing of the sort. I assume you realize that--it's obvious--and are simply being disingenuous by pretending that was being claimed.

Whether adding a new particle or an entire proposed theory is more speculative is a matter of opinion.

I agree that SOMETHING here is a matter of opinion. In my opinion classical GR because it blows up at high density is an incomplete theory that works beautifully at low density and it needs to be completed by discovering its quantum version. There is a widely shared belief that quantizing GR will eliminate the singularity, and I see people working on various ways to do that. This theoretical work can be called "speculative". I see nothing wrong with that. I expect the various lines of theoretical development to arrive at various predictions testable by observation. That's my PoV, anyone else is welcome to differ. As you say it is a matter of opinion :w

 

[marcus]

But don't you effectively need something like it to create the bounce? That is, don't you need something with the same sort of equation of state at the classical level as an "inflaton" (and a very different equation of state from ordinary matter or radiation) to create the bounce?...

That's an interesting idea, Peter.
You certainly don't in the Loop bounce case. But I'm not expert and there are a number of different bounce cosmologies. Maybe one or more of them involve some kind of exotic matter that has an equation of state that causes the bounce.
When you say "effectively" need something (like an inflaton field) it gives some latitude, though.

I wonder.

To take the Loop bounce as an example, as I recall it goes back to 1999-2000. and then was reformulated around 2005. I've never seen mention of an "effective' particle or field that would imitate the effect of just quantizing GR geometry. Instead it goes something like this (hand-wavingly) when geometry is quantized the area operator turns out to have discrete spectrum. There is a minimum positive area. But curvature is inverse area. So there is a maximum curvature. GR translates that into a maximum density.

Then after a lot of equations a quantum corrected version of the Friedmann equation is derived. This essentially says that gravity repels at Planck scale density. There is a term in the equation that is opposite the classical one and density dependent, suppressed by Planck density. You see a term that is minus ρ/ρ_Planck in the Friedmann equation.

One intuitive explanation that is sometimes given is that when it is quantized, geometry itself has a Heisenberg uncertainty principle---it resists being infinitely pinned down.

I've never seen this described by using an equivalent matter field. But Robert Brandenburger's group has a different approach called "matter bounce" which uses something called "Mukhanov-Sasaki equation". It doesn't say there is an exotic matter like an "inflaton", but somehow they get a bounce. I guess with ordinary matter, maybe it involves the Heisenberg uncertainty principle. I haven't studied this. Hope this brief comment is helpful. :)

 

[Chalnoth]

I agree that SOMETHING here is a matter of opinion. In my opinion classical GR because it blows up at high density is an incomplete theory that works beautifully at low density and it needs to be completed by discovering its quantum version. There is a widely shared belief that quantizing GR will eliminate the singularity, and I see people working on various ways to do that. This theoretical work can be called "speculative". I see nothing wrong with that. I expect the various lines of theoretical development to arrive at various predictions testable by observation. That's my PoV, anyone else is welcome to differ. As you say it is a matter of opinion :w

Until they can prove that the semi-classical limit of their chosen quantum gravity model is actually General Relativity, I don't think it's really a great idea to take the results too seriously.

 

[marcus]

@ Peter,
I'm delighted if anyone wants to look into some of the other bounce cosmology approaches. I'll give a link or two:
http://arxiv.org/abs/1206.2382
Towards a Nonsingular Bouncing Cosmology
Yi-Fu Cai, Damien A. Easson, Robert Brandenberger

Cai and Brandenburger are associated with the "matter bounce" idea which has also been taken over by Sergei Odintsov. Edward Wilson-Ewing seems to have been engaged recently in building bridges between other nonsingular (bounce) cosmologies and Loop. Here are a couple of his:

http://arxiv.org/abs/1211.6269
The Matter Bounce Scenario in Loop Quantum Cosmology
Edward Wilson-Ewing

http://arxiv.org/abs/1306.6582
Ekpyrotic loop quantum cosmology
Edward Wilson-Ewing
(Submitted on 27 Jun 2013)
We consider the ekpyrotic paradigm in the context of loop quantum cosmology. In loop quantum cosmology the classical big-bang singularity is resolved due to quantum gravity effects, and so the contracting ekpyrotic branch of the universe and its later expanding phase are connected by a smooth bounce. Thus, it is possible to explicitly determine the evolution of scalar perturbations, from the contracting ekpyrotic phase through the bounce and to the post-bounce expanding epoch. The possibilities of having either one or two scalar fields have been suggested for the ekpyrotic universe, and both cases will be considered here. In the case of a single scalar field, the constant mode of the curvature perturbations after the bounce is found to have a blue spectrum. On the other hand, for the two scalar field ekpyrotic model where scale-invariant entropy perturbations source additional terms in the curvature perturbations, the power spectrum in the post-bounce expanding cosmology is shown to be nearly scale-invariant and so agrees with observations.
11 pages

 

[PeterDonis]

When you say "effectively" need something (like an inflaton field) it gives some latitude, though.

Yes. See below.

There is a term in the equation that is opposite the classical one and density dependent, suppressed by Planck density.

In other words, the effective equation that governs the dynamics does change. Which it has to, since we know that the standard classical equation (the Friedmann equation without any non-classical terms added) leads to a singularity. That's all I was trying to say.

I'll take a look at the papers you linked to; they look interesting.