Question about detailed specifics of inflation

[phinds]

In researching inflation, I have found on various web sites, significantly different numbers regarding

when did inflation start? (10E-35, 10E-28, 10E-33, etc)

when did inflationi end? (10E-33, 10E-38, etc)

what was the change in the diameter of the U during inflation? (10E40, 10E35, 10E52, 10E78 etc)

what was the size of the U when inflation started (I forgot to note these but I recall there were some different ones).

Is there any agreement or any recognized authority for these numbers and if so, can you give me a reference? Is it perhaps that case that these are all progressive refinements of the values and there is a recent and agreed-upon set of values? If I recall correctly, the first of the listed numbers is in each case the one attributed to Guth but I did not even note where the rest of them came from and I don't know but what these might be early Guth numbers that he has since refined.

I just got The Inflationary Universe a couple of days ago and haven't looked at it yet. Is he still considered THE expert on this?

 

[bapowell]

when did inflation start? (10E-35, 10E-28, 10E-33, etc)

This is not a very useful number, and is frankly not known. The end of inflation, called reheating, when all the inflationary energy turns into hot radiation, is what is referred to as the hot big bang by modern cosmologists. So, it's more correct to think in terms of the chronology: inflation -> big bang rather than big bang -> inflation. It's more appropriate to talk about the energy scale at which inflation began. Then, if you wish to extrapolate from this energy back to the Planck energy assuming a standard, radiation dominated universe, you can obtain the time at which it started. Bu this assumes 1) a standard radiation dominated universe before inflation 2) that there every was a time when the Planck energy was achieved. So, anytime you see times quoted for inflation, these things are assumed.

what was the change in the diameter of the U during inflation? (10E40, 10E35, 10E52, 10E78 etc)

You must be careful with your terminology here. There are two things that typically grow as the universe expands: the scale factor -- which measures the distance between two points in space (think grid marks painted on the surface of a rubber sheet as it expands), and the diameter of the observable universe. During inflation, the scale factor grows by a vast amount, at least by a factor of exp(60) or so, but perhaps very much more. But the size of the observable universe, set by the Hubble parameter as $H^{-1}$, scarcely grows at all during this time. Since we don't know by how much the universe expanded during inflation, we don't know how long it inflated for, so it's impossible to put a time on it. We also don't know what the energy was when inflation started: it could be anywhere from the electroweak scale (100s of GeV) all the way up to the GUT scale (10^15 or 10^16 GeV). So any numbers you see quoted regarding times, expansion rates, or sizes of the universe involve some assumption about these important details.

what was the size of the U when inflation started (I forgot to note these but I recall there were some different ones).

Small. But again, it depends on what quantity you're talking about. If you are referring to the scale factor, than if the scale factor = 1 today, then it was at least a factor of exp(60) smaller at the start of inflation. If you're talking about the size of the causal universe at the time of inflation, this again is given by $H^{-1}$ which is set by the energy scale at which inflation began.

I just got The Inflationary Universe a couple of days ago and haven't looked at it yet. Is he still considered THE expert on this?

Guth is still the man. But there are plenty of other experts: Linde, Liddle, Lyth, Kolb, Turner, Steinhardt, Vilenkin, the list goes on and on.

 

[phinds]

Thank you for that detailed reply. Very helpful, particularly the distinction between the growth of the scale factor and the growth in size of the U.

One question in response. I have read that "big bang" is taken to mean (1) the singularity itself, which is mystery, and then (2) the inflationary period, or the "BB period".

I take it from your response that #2 is not "standard" terminology (to the extent that there IS a standard) but rather that #2 should be "the time FROM the end of inflation forward", not the time OF the infaltionary period, yes?

Thanks again.

 

[bapowell]

I take it from your response that #2 is not "standard" terminology (to the extent that there IS a standard) but rather that #2 should be "the time FROM the end of inflation forward", not the time OF the infaltionary period, yes?

Pretty much. You are correct that the term Big Bang has enjoyed different meanings, particularly to different people. It is OK to connect the term to the initial singularity (with the caveat that this is a purely mathematical interpretation), but this is not the operative use of the term by modern cosmologists. By "Big Bang" most cosmologists are referring to the model rather than the event. The Big Bang model is the currently accepted view of a universe expanding from an earlier hot, dense phase. This view, as stated, is valid with or without inflation. If one includes a bout of inflationary expansion, then when inflation ends the universe must reheat. It does this through the decay of the energy that drove the inflation: this energy gets dumped into a hot bath of radiation, which then undergoes nucleosynthesis, decoupling, CMB, galaxy formation, and so on -- all the features of the standard Big Bang model. So inflation can be correctly thought of as pre-dating the events that make up the thermodynamic history of the universe.

 

[phinds]

I had read about the events you just stated, but I did not quite have it in full context of modern theory, so again, you have been very helpful. Thanks. Part of my problem is that my reading has been somewhat chaotic rather than systematic. I have, at least, gotten past the point of screaming "THAT'S NOT *$^#%% POSSIBLE" all the time and am now, to paraphrase Twain, able to believe 3 impossible things before breakfast.