Temperature at beginning of Electroweak Epoch?

[Stan Stuchinski]

Now, I understand that any discussion of the very early Universe is entirely hypothetical and to say it is extremely speculative is being generous. However, there are a few concepts regarding the Grand Unified Epoch, the Inflationary Epoch, and the Electroweak Epoch that I am hoping someone will have the patience to explain…

According to http://en.wikipedia.org/wiki/Inflation_(28cosmology)

“Reheating”
“Inflation is a period of supercooled expansion, when the temperature drops by a factor of 100,000 or so. (The exact drop is model dependent, but in the first models it was typically from 10^27K down to 10^22K.) This relatively low temperature is maintained during the inflationary phase. When inflation ends the temperature returns to the pre-inflationary temperature; this is called reheating or thermalization because the large potential energy of the inflaton field decays into particles and fills the Universe with Standard Model particles, including electromagnetic radiation, starting the radiation dominated phase of the Universe.”​

My question is this: If, “during the period of supercooled expansion during the Inflationary Epoch the temperature dropped from 10^27K down to 10^22K, and when inflation ends the temperature RETURNS to the pre-inflationary temperature in the process called reheating...”

Does mean that, at the beginning of the next epoch – the Electroweak Epoch – the temperature ROSE BACK TO 10^27K (the temperature at the start of Inflation)? If that is correct, then what would the temperature have been at the END of the Electroweak Epoch?

Thanks in advance for your time and consideration,

Stan

 

[Chalnoth]

In these inflation models, the temperature increase is caused by the decay of the inflaton field. The temperature immediately after inflation is set by the energy density of this field.

Later in the expansion, the temperature gets a boost every time a particle becomes non-relativistic (or more precisely, the temperature is prevented from falling for a short time while the particle's matter/anti-matter pairs annihilate).

 

[Stan Stuchinski]

In these inflation models, the temperature increase is caused by the decay of the inflaton field. The temperature immediately after inflation is set by the energy density of this field.

Later in the expansion, the temperature gets a boost every time a particle becomes non-relativistic (or more precisely, the temperature is prevented from falling for a short time while the particle's matter/anti-matter pairs annihilate).

Thank you for responding to my query, Chalnoth, It is much appreciated. However...

I DO understand that, as you state, "In these inflation models, the temperature increase is caused by the decay of the inflaton field." However, what I'm after is precise (and I understand that this can only be speculation) NUMBERS i.e.: if the temperature dropped from 10^27K down to 10^22K DURING the Inflationary Epoch, what would the temperature have risen to after the inflaton field decayed at the start of the next epoch, the hypothesized Electroweak Epoch? Can it be said that the temperature rose all the way BACK up to 10^27K?

Thanks again, and have a great day,

Stan

 

[Chalnoth]

Depends upon the model. But typically inflationary models end up at extraordinarily low temperatures near the end of the inflationary epoch (as in, a tiny fraction of a Kelvin, not $10^{22}$K).

There really isn't necessarily a link between the original temperature of the system when inflation began and the temperature after reheating. The temperature when the system began is highly model-dependent, and could conceivably be close to zero.

To sum up:
1. The temperature after reheating is set by the energy density of the inflaton field.
2. The temperature at the beginning of inflation is set by the specific model that starts inflation, and can be virtually anything in principle.
3. The ratio of temperature between the beginning of inflation and the end just before reheating is set by the amount of expansion that has transpired. Typical models require an expansion by a factor of around $e^{70}$, or $10^{30}$, which is the factor by which the initial temperature is divided.

 

[Chronos]

As Chalnoth noted, the temperature of the universe following reheating is uncertain. See http://arxiv.org/abs/hep-ph/0005123, Largest temperature of the radiation era and its cosmological implications, for discussion.

 

[Stan Stuchinski]

As Chalnoth noted, the temperature of the universe following reheating is uncertain. See http://arxiv.org/abs/hep-ph/0005123, Largest temperature of the radiation era and its cosmological implications, for discussion.

Thanks much, Chalnoth and Chronos. Your time is greatly appreciated.

Yes, I DO understand that any numbers are inherently "model dependent." However, WikiPedia got their numbers SOMEWHERE. (I am assuming the model used to be Glashow's SO(5) model.) So I guess what I am asking is...

"Using WikiPedia's figures of 27^10K at the beginning of Inflation and 10^22K at the end of Inflation, what would the temperature have risen to at the beginning of the Electroweak Epoch, and what would the temperature have been at the end of the Electroweak Epoch?"​

Thanks again for your courtesy, my friends, and have a great day!

Stan

 

[Chalnoth]

As far as end of the electroweak epoch, the neutrinos freeze out at a temperature of about 1MeV (about $10^{10}$K). This doesn't really impact the temperature of the universe at the time, because the effect of the freeze out (called "neutrino decoupling") is that the neutrinos stop interacting with other matter to any significant degree.

 

[Stan Stuchinski]

I concur that neutrino decoupling took place at a temperature of 1Mev (about 10^10K), but I was under the impression that neutrino freeze-out occurred at 1 second ATBB (after the Big Bang). Would this not place neutrino decoupling at the end of the Hadron Epoch (10^-6 to 1 second ATBB), rather than at the end of the Electroweak Epoch? In fact, did not the Quark Epoch precede the Hadron Epoch (10^-12 to 10^-6 second ATBB)? And the Electroweak Epoch began even earlier, as I understand it, at the end of Inflation (at 10^-32 seconds ATBB).

Stan

 

[Chalnoth]

Ah, yes, you're right. I took the end of the electroweak epoch to mean the end of the period where weak-force interactions were common (i.e., before neutrino decoupling). But the usual definition is that it was the epoch when the weak and electromagnetic forces were indistinguishable components of a larger superforce, which ended at about 100GeV.

At those temperatures, the W and Z bosons would have been relativistic, so the end of the electroweak epoch would have gotten a boost in temperature from the decay of any W and Z bosons. I'm not sure there would have been all that many around, however, as they have a half-life of about $10^{-25}$s, which is extremely short compared to the lifetime of the universe at the time which was about $10^{-12}$s.