Big Bang Cosmology: Running Hot and Cold

[Jeltz]

Any literature on the big bang usually describes the initial moments as hot and dense. The laws of thermodynamics point to a universe where entropy is increasing, so given the assumption the universe is a thermodynamically isolated system, this implies a low entropy big bang. given that minimum entropy is irrevocably associated with absolute zero, how can the big bang be both hot and cold at the same time? I have thought about this over many years and have only ever come up with one way that this apparent paradox can be resolved.

Can anyone describe to me simply what standard big bang cosmology has to say on this matter?

 

[collinsmark]

Hello Jeltz,

Welcome to Physics Forums!

The brief period inflation soon after the big-bang is the key. The end result of inflation is that it left matter more-or-less evenly distributed throughout the universe (as it was then [and even still is now on the scale of galaxy clusters]).

When it comes to most other forces, evenly spread out matter corresponds to high entropy. An example is gas particles in a room. If you could gather all the gas molecules in a room into a small spot in one corner, the result would be well ordered, and have low entropy. Allowing the gas to fill the room evenly (at it does naturally) increases the entropy.

Gravity works in the opposite way. An even distribution of particles have the lowest entropy where gravity is concerned. As gravity pulls matter into clumps, entropy increases. Black holes are the highest entropy that is possible to fit in a given volume (the volume within the back hole's event horizon). It's not possible to increase the entropy of a black hole without making it bigger.

On large scales gravity dominates. So on large scales, evenly distributed matter corresponds to overall low entropy. And the brief inflationary period is to thank for the reason why we live in a universe with relatively low entropy. In other words, the inflationary period is to thank for why we live in such a well ordered universe. Well, according to the theory that is.

 

[Chronos]

The initial state of the universe was, as it is now, spatially unbounded.

 

[Chalnoth]

On large scales gravity dominates. So on large scales, evenly distributed matter corresponds to overall low entropy. And the brief inflationary period is to thank for the reason why we live in a universe with relatively low entropy. In other words, the inflationary period is to thank for why we live in such a well ordered universe. Well, according to the theory that is.

Bear in mind that inflation doesn't really answer this problem, because inflation must begin with an even lower-entropy state.

 

[Jeltz]

Thanks collinsmark for a succinct explanation of the status quo. My understanding is that at the present inflation is a theoretical construct necessary to best explain observations but has not yet been shown to be either a provable consequence of GR or QM or incompatible with them?

I presume Chronos in saying that the universe is unbounded should be taken in the mathematical sense of "having no boundary" as the surface topology of a ball has no boundary, and in fact is saying the big bang/universe is indeed an isolated system from a thermodynamic viewpoint and that this is the current status-quo consensus.

I have noticed a lot of confusion in this forum over terms like finite/infinite bounded/unbounded closed/open which in fact have subtly different mathematical meanings compared to common English usage meanings. Closed/open indeed have quite different meanings for cosmologists, mathematicians and common english usage. Surely we should use this forum to at least agree on a common set of terminology?

 

[collinsmark]

Bear in mind that inflation doesn't really answer this problem, because inflation must begin with an even lower-entropy state.

I don't think it's quite as simple as that. On the other hand, maybe it is that simple if all factors are considered, and considered correctly. But my point is that this is no simple problem. In normal thermodynamics problems that we are accustomed to in our everyday world, we can calculate the change in entropy of a system as the volume increases. But in these situations, the system's volume is increasing into space. I.e. increasing into pre-existing space. But in an inflationary system (particularly the brief, initial inflation that happened soon after the big bang), it is space itself that is increasing in volume, by many, many orders of magnitude in tiny amount of time. Again, the difference is that in the first scenario, the system is increasing into space. In the latter (inflationary case) it is space itself that is increasing, carrying any and all mass/energy particles along with it. It's a game changer in the way thermodynamics is approached (such as the way in which one defines a given volume of space).

I do not contend to be an expert on this subject (as I certainly am not). In my original post I was simply attempting to point the OP in the right direction, if curious about further research.

Here is a link to a paper that could probably explain things better than I can.
http://iopscience.iop.org/0264-9381/8/8/001"
I haven't read it myself (you have to pay for it), but judging by the abstract it seems to be on topic. It's a rather old article, before the discovery of the present day "accelerating" universe. It was written back when the "big crunch" seemed as likely a scenario as any. So the article is a bit dated.

 

[Chalnoth]

I don't think it's quite as simple as that.

This is a well-known result. Basically, because the universe during inflation would have had behavior very close to a cosmological constant, one can use the known entropy of De Sitter space to approximate the change in entropy of a region of space-time during inflation. What you get is that the entropy of a region of De Sitter space is proportional to the area of the horizon. Since, during inflation, you go from one small region to many, and since the horizon scale stays approximately the same, the entropy increase goes as approximately the increase in volume.

So you end up with a mind-bogglingly massive increase in entropy during inflation. Reheating produces a further increase in entropy of the system.

This really shouldn't be a surprise, of course: for there to be an arrow of time at all, you need an increase in entropy. Inflation wouldn't make any sense if entropy decreased as it went forward in time. As I've stated elsewhere, this would actually be a contradiction in terms. Inflation solves other problems with the big bang, but it alone does not solve the requirement of very special initial conditions.

 

[collinsmark]

This really shouldn't be a surprise, of course: for there to be an arrow of time at all, you need an increase in entropy. Inflation wouldn't make any sense if entropy decreased as it went forward in time.

Sounds reasonable.

 

[collinsmark]

Okay, I've been thinking about this a day now, and I realize that I might not have been clear in my earlier post. Let me just start over and allow me to reword my point.

I interpreted the OP's question as the following. Forgive me if I am misinterpreting, but let me paraphrase, adding in my own assumptions. "According to theory, the early universe was hot and dense, which corresponds to high entropy. But today's universe seems much colder and less dense, corresponding to lower entropy. The laws of thermodynamics states that entropy must always increase. So where is the disconnect?"

I mentioned earlier that the laws of thermodynamics are not violated, but you have to be very careful on how you treat volume. If you consider a chuck of expanding space, the entropy of that space increases as it expands. Chalnoth describes this very well. But here, "apples to apples" means chunk of space before, to the same chunk of space after. And volumes are not equal, because the space expanded. The "volume after" is much greater than the "volume before".

But my earlier point was that due to the expanding universe a given constant volume of space can have lower entropy now than it had in the past (not necessarily in general, but at times of very fast expansion). For example, measure the entropy of a meter cubed volume of the early universe, and compare that to a meter cubed volume of typical space now. Or more appropriately, consider the volume of what is now our observable universe. Measure the entropy within that volume of the very, very early universe and compare that to the entropy of today's observable universe. The entropy within that constant volume has decreased. And this is due to the expanding universe. Throughout the history of the universe, entropy as a whole has always increased, but at the times of fast expansion, entropy per unit volume has decreased (I'm limiting this to times of fast expansion, by the way).

The inflationary period is quite special, by the way. Due to the intense negative pressure, a vast amount of matter/energy was actually created during cosmic inflation (according to most inflationary theories anyway), which of course contributes to entropy. But at the same time, space greatly expanded too, such that the entropy per unit volume (constant volume here) actually decreased, giving us our apparent low-entropy observable universe.

And the key here is that during the early cosmic inflation matter/energy was created homogeneously, which is the lowest entropy configuration from the gravitational perspective. Allow me to comment on Chalnoth's post directly.

What you get is that the entropy of a region of De Sitter space is proportional to the area of the horizon. Since, during inflation, you go from one small region to many, and since the horizon scale stays approximately the same, the entropy increase goes as approximately the increase in volume.

You're right that you go from one region of space to many (all filled with matter/energy). But the new space is not a replica of the old. The original space (at a smaller volume) may have been quite clumpy (higher entropy). But the new space is increasingly populated with matter/energy homogeneously, giving it lower entropy per unit volume.

I like the analogy that Brian Greene, a theoretical string theory physicist, gives in his book The Fabric of the Cosmos (Space, Time, and the Texture of Reality)

[...] The total entropy increased, just as we expect from the second law.
...But, and this is the important point, the inflationary burst, by smoothing out space and ensuring a homogeneous, uniform, low-entropy gravitational field, created a huge gap between what the entropy contribution from gravity was and what it might have been. Overall entropy increased during inflation, but by a paltry amount compared to with how much it could have increased. It's in the sense that inflation generated a low-entropy universe: by the end of inflation, entropy had increased, but by nowhere near the factor by which the spatial expanse had increased. If entropy is likened to property taxes, it would be as if New York City acquired the Sahara Desert. The total property taxes collected would go up, but by a tiny amount compared with the total increase in acreage.

Does that make more sense?

 

[Chalnoth]

Yes, and that likely has something to do with the solution to the problem. It isn't complete, however, for a few reasons:

1. It doesn't actually explain the low entropy initial conditions. The small region from which our much larger region arose is still a different configuration of the same system, so the question remains.
2. Inflation actually requires the region to be quite smooth to even get started. Any deviations from smoothness get removed during inflation, of course, but it has to start pretty smooth anyway.
3. Entropy density doesn't actually decrease much during inflation. It does decrease later on, but not a whole lot during inflation. The fact does remain that the current entropy density is very low, and will tend to get lower.

So, there are a couple of ways you can go about trying to solve the problem. First, you can try to discover some dynamics under which the start of inflation is actually generic. This is being attempted, for example, by the loop quantum cosmology people. They show that if you have a collapsing universe, you automatically get a bounce that includes inflation. The problem, as near as I can tell, is that they assume that the collapsing universe is itself quite smooth, which seems to me a very unphysical assumption. Personally, I suspect that this direction of inquiry is doomed to failure, because the thermodynamic arguments for the low-entropy condition of our early universe are quite independent of any specific theory or model of the early universe.

Another direction from which we might attempt to solve the issue is to tie the low entropy density late universe to the low total entropy early universe. One potential way of doing this was proposed by Sean Carroll and Jennifer Chen a few years back:
http://arxiv.org/abs/gr-qc/0505037

 

[Jeltz]

OK I have been thinking on this for a few days now. We will inevitably end up going in circles until the smoothness of the manifold in GR is reconciled with the non-smooth nature of quantum fluctuations. I presume when this is done correctly, the root cause of inflation will become clear.

I have also found Abhay Ashtekar's views on these subjects to provide some good explanations for a lay person from an expert on this subject.

http://gravity.psu.edu/people/Ashtekar/

I have also written some un-reviewed work of my own on

http://jonkers.net.au/funstuff/funstuff.aspx

 

[shomas]

This thread on entropy has made me wonder about the universe's level of entropy just before photon decoupling and compare that with the level of entropy just after

its assumed that just before photon decoupling the distribution of matter and energy was quite homogeneous, therefor the ability to extract energy from higher concentrations in order to do work would have been quite small. After matter went though a phase transition, matter was free to gather and form the precursors to galaxies, condense and give off heat and eventually fusion. odd how it seems as if the expanding caused a decrease in entropy at that moment.

 

[Chalnoth]

This thread on entropy has made me wonder about the universe's level of entropy just before photon decoupling and compare that with the level of entropy just after

its assumed that just before photon decoupling the distribution of matter and energy was quite homogeneous, therefor the ability to extract energy from higher concentrations in order to do work would have been quite small. After matter went though a phase transition, matter was free to gather and form the precursors to galaxies, condense and give off heat and eventually fusion. odd how it seems as if the expanding caused a decrease in entropy at that moment.

Gravitational collapse is not a decrease in entropy, but rather an increase. Gravitational collapse was also occurring before recombination.