Random Walk Question re Inflation

[Buzz Bloom]

I have been puzzled about the possible interaction mechanisms among the various particles during inflation that would have performed the mixing of mass-energy (ME) required for the uniformity of the CBR. Here is my understanding about what must happen to acheve the necessary mixing of ME during inflation.

At the time when inflation starts, say t_s, let D_s be the length of the diameter then of the space that now is our observable universe. Let A and B the pair of points at opposite ends of an arbitrary diameter. The distance between A and B is _Ds. Assume two regions of space of the same size, one surrounding A and one surrounding B, say R_A and R_B respectively, have MEs respectively E_A and E_B. Assume E_A has significantly greater ME than significantly greater than E_B.

To solve the horizon problem, during inflation, (1/2) (E_A - E_B) of ME must move from R_A to R_B.

It seems to me unreasonable to assume that the ME movement from the R_A to R_B happens by means of particles moving directly from R_A to R_B without interacting with any particles along the way. The question then arises: what is the expected mean free path (MFP) of these particles. As the universe expands, the MFP will of course also increase. So, the path of ME from R_A to R_B will require a number of particle interations along the way, say on the average N_avg. (An estimate of N_avg would have to be calculated taking the expansion of the universe into account.)

It seems reasonable that the path ME travels would be a random walk. In a non-expanding space, the effective speed of a random walk would proportional to the square-root of the number of steps: √N_avg. Therefore, if particles move at speed c (with an adjustment for the expansion) , the effective speed of ME moving from A to B would be c/√N_avg, (similarly adjusted).

Can anyone point out a flaw in this random walk concept regarding inflation?

Can anyone suggest a source about inflation that discusses this issue about a random walk?

 

[Chalnoth]

There is no mixing of mass-energy during inflation, at least not any that makes any difference. Inflation dilutes the universe so dramatically that there is no reason to believe that there were any particles left within our past horizon except for those that make up the field that drove inflation. Once inflation ends, the nearly-uniform inflaton particles decay, producing a hot soup of particles which eventually cool to become the matter that makes up our universe today.

 

[Buzz Bloom]

Inflation dilutes the universe so dramatically that there is no reason to believe that there were any particles left within our past horizon except for those that make up the field that drove inflation. Once inflation ends, the nearly-uniform inflaton particles decay, producing a hot soup of particles which eventually cool to become the matter that makes up our universe today.

Hi @Chalnoth:

Thanks for your very helpful post.

The Wikipedia article https://en.wikipedia.org/wiki/Inflaton says:
The basic process of inflation consists of three steps:

1. Prior to the expansion period, the inflaton field was at a higher-energy state.
2. Random quantum fluctuations triggered a phase transition whereby the inflaton field released its potential energy as matter and radiation as it settled to its lowest-energy state.
3. This action generated a repulsive force that drove the portion of the universe that is observable to us today to expand from approximately 10⁻⁵⁰ meters in radius at 10⁻³⁵ seconds to almost 1 meter in radius at 10⁻³⁴ seconds.​

This seems to be consistant with your answer. I interpret both the Wikipedia text and your answer to say:

From the end of the Planck epock through the beginning of inflation, that part of the universe that has now become our current observable universe contained the inflaton field and nothing else.​

Is this interpretation correct?

Does this Wikipedia text seem to you to be a correct summary of inflation? If not, where do you differ from it? (I note that another Wikipedia article, https://en.wikipedia.org/wiki/Inflaton , gives different times for the beginning and end of inflation.)

TheWikipedia Inflaton artical also says:

It is suggested that the Higgs boson might act as the inflaton.​

Does this possibility seem plausible to you?

Regards,
Buzz

 

[Chalnoth]

Hi @Chalnoth:

Thanks for your very helpful post.

The Wikipedia article https://en.wikipedia.org/wiki/Inflaton says:
The basic process of inflation consists of three steps:

1. Prior to the expansion period, the inflaton field was at a higher-energy state.
2. Random quantum fluctuations triggered a phase transition whereby the inflaton field released its potential energy as matter and radiation as it settled to its lowest-energy state.
3. This action generated a repulsive force that drove the portion of the universe that is observable to us today to expand from approximately 10⁻⁵⁰ meters in radius at 10⁻³⁵ seconds to almost 1 meter in radius at 10⁻³⁴ seconds.​

This seems to be consistant with your answer. I interpret both the Wikipedia text and your answer to say:

From the end of the Planck epock through the beginning of inflation, that part of the universe that has now become our current observable universe contained the inflaton field and nothing else.​

Is this interpretation correct?

This doesn't seem to be a very good Wikipedia page. The page on Inflation itself is much better:
https://en.wikipedia.org/wiki/Inflation_(cosmology)

Shortly after inflation began, everything else that may have been around before inflation gets pushed so far apart that it's unlikely to find a single particle from the pre-inflation era within our visible universe. Thus just before inflation ended the inflaton made up essentially everything in our universe. This effect is discussed in the magnetic monopole problem section:
https://en.wikipedia.org/wiki/Inflation_(cosmology)#Magnetic-monopole_problem

I would like to stress that because of this feature of inflation, it tends to wipe out all evidence of anything that occurred prior to a certain point, which means that discussion of a "Planck epoch" is troublesome as the post-inflation universe has nothing to do with what happened between a hypothetical "Planck epoch" and the start of inflation, and in fact there may have never been a Planck epoch in the first place.

Also, the second point in that checklist on the Wikipedia page is either very confusingly-worded or just plain wrong. Inflation begins with a small region of space-time (possibly smaller than a proton in size) where the inflaton field takes on a potential value such that inflation can start. Sometimes this is achieved through some kind of quantum tunneling event, but there are many competing models. However it starts, once it starts the inflaton field acts in such a way that its field value tries to settle into a lower-energy state, but the expansion of the universe acts as a sort of "friction" that slows the field's progress. So the field keeps close to the same value as it expands, leading to a nearly constant energy density. A constant energy density produces an exponential expansion.

Inflation isn't quite exponential, because the field value isn't completely constant. The field's potential energy slowly drops over time as the field settles. When it reaches the field minimum, it oscillates around the minimum, which causes the field to decay into various energetic particles (including normal matter and dark matter).

 

[Buzz Bloom]

Hi @Chalnoth:

Thank you very much for your post. It was both helpful and amusing. I particularly liked your summary and reference to the Magnetic Monopole Problem. The following Wikipedia article quote gave me quite a big belly laugh,

Though, as cosmologist Martin Rees has written, "Skeptics about exotic physics might not be hugely impressed by a theoretical argument to explain the absence of particles that are themselves only hypothetical. Preventive medicine can readily seem 100 percent effective against a disease that doesn't exist!
​

Also, your statement that inflation

tends to wipe out all evidence of anything that occurred prior to a certain point, which means that discussion of a "Planck epoch" is troublesome as the post-inflation universe has nothing to do with what happened between a hypothetical "Planck epoch" and the start of inflation, and in fact there may have never been a Planck epoch in the first place

in my mind seems to put (1) the controversial inflation concept into a possibly controversial conflict with (2) the Standard Model's need for a Planck epoch to highlight the non-controversial conflict between QM and GR at the very earliest stage of the universe.

It seems to me that the Planck epoch is a better much fit with Occam's razor than inflation. Do you know of any non-controversial logical reason why presently unknown (and possibly unknowable) phenomena that might have occurred during the Planck epoch could not be plausible solutions to the flatness problem, the horizon problem, and the monopole problem (as well as the problem of other undetected GUT predicted very heavy particles)?

Regards,
Buzz

 

[Chalnoth]

Hi @Chalnoth:

Thank you very much for your post. It was both helpful and amusing. I particularly liked your summary and reference to the Magnetic Monopole Problem. The following Wikipedia article quote gave me quite a big belly laugh,

Though, as cosmologist Martin Rees has written, "Skeptics about exotic physics might not be hugely impressed by a theoretical argument to explain the absence of particles that are themselves only hypothetical. Preventive medicine can readily seem 100 percent effective against a disease that doesn't exist!​

​

Magnetic monopoles aren't as unlikely as you might think. They arise from a very simple idea: the math that describes the fundamental laws should be simple.

Right now, the standard model of particle physics is described by the symmetry SU(3) x SU(2) x U(1). Here SU(3) is the strong nuclear force, SU(2) is the weak nuclear force, and U(1) is the electromagnetic force. Never mind the definition of these symmetry groups, but just pay attention that this description is pretty complicated.

It turns out that you can simplify the whole thing if the true, fundamental laws follow a different, higher-order symmetry, and the SU(3) x SU(2) x U(1) structure is recovered by physical processes later on. There are lots of candidates here (SU(5), SO(10), SU(8), O(16), etc.), and you can read more about them at this Wikipedia page. But one thing that they all have in common is that they all predict the existence of magnetic monopoles. You just can't have a simpler fundamental theory than SU(3) x SU(2) x U(1) without them.

​

Also, your statement that inflation

in my mind seems to put (1) the controversial inflation concept into a possibly controversial conflict with (2) the Standard Model's need for a Planck epoch to highlight the non-controversial conflict between QM and GR at the very earliest stage of the universe.

The standard model doesn't need a Planck epoch. It's true that at Planck temperatures, we would need a theory of quantum gravity to describe how the universe behaves.

In fact, not needing to go all the way back to the Planck epoch is a beneficial feature of Inflation: since we don't know precisely how to unify gravity and quantum mechanics, inflation can potentially work well with whatever happens at those extremely high temperatures.

It seems to me that the Planck epoch is a better much fit with Occam's razor than inflation. Do you know of any non-controversial logical reason why presently unknown (and possibly unknowable) phenomena that might have occurred during the Planck epoch could not be plausible solutions to the flatness problem, the horizon problem, and the monopole problem (as well as the problem of other undetected GUT predicted very heavy particles)?

If the best you've got is, "Maybe something in unknown physics solves this problem," then you don't have any answer at all. The response to this is simply, "What is the specific model of the Planck epoch that you're going to use that solves this problem?" "Maybe there's a model out there," isn't good enough.

 

[Buzz Bloom]

"Maybe there's a model out there," isn't good enough.

Hi Chalnoth:

I humbly accept with chagrin the education your post gives me. I confess that my reluctance to embrace inflation is more aesthetic than scientific.

Regards,
Buzz

 

[Buzz Bloom]

Also, the second point in that checklist on the Wikipedia page is either very confusingly-worded or just plain wrong. Inflation begins with a small region of space-time (possibly smaller than a proton in size) where the inflaton field takes on a potential value such that inflation can start. Sometimes this is achieved through some kind of quantum tunneling event, but there are many competing models. However it starts, once it starts the inflaton field acts in such a way that its field value tries to settle into a lower-energy state, but the expansion of the universe acts as a sort of "friction" that slows the field's progress. So the field keeps close to the same value as it expands, leading to a nearly constant energy density. A constant energy density produces an exponential expansion.

Hi @Chalnoth:

Sorry to bother you again with my ignorance. I have been thinking about this for a while now.

The quoted description of the inflation mechanism is very clear and reasonable. However, one of the issues I am interested in is not discussed. Here are two new questions.

(1) Why is the distribution of the inflation field's energy uniform, as it needs to be for inflation to solve the horizon problem?

(2) Why can't the reason for the uniformity of the inflation field's energy also be applied as a mechanism which could make the distribution of the early energy of the stuff of our universe uniform without inflation?​

Regards,
Buzz

 

[Chalnoth]

Hi @Chalnoth:

Sorry to bother you again with my ignorance. I have been thinking about this for a while now.

The quoted description of the inflation mechanism is very clear and reasonable. However, one of the issues I am interested in is not discussed. Here are two new questions.

(1) Why is the distribution of the inflation field's energy uniform, as it needs to be for inflation to solve the horizon problem?​

(2) Why can't the reason for the uniformity of the inflation field's energy also be applied as a mechanism which could make the distribution of the early energy of the stuff of our universe uniform without inflation?​

Regards,
Buzz

Unfortunately, there is no explanation for this, so inflation doesn't really solve the horizon problem so much as shift the horizon problem back. However, the degree of required uniformity is much, much smaller in inflation than it is with the classical big bang: now we only need uniformity over a distance much smaller than the size of a proton, rather than the uniformity over millions of light years required by the classical big bang. This makes it seem more plausible that inflation might arise from some sort of random fluctuation.