# Fluctuations in the cosmological equation of state during the radiation dominated era

The radiation dominated era is described as a universe full of photons and ultra-relativistic particles with little slow moving matter. Ideally it has w = P/ρ = 1/3.

But didn't the actual value of w move down and up over this era? My reasoning is as follows: When the temperature gets within an order of magnitude of a particle's mass said particles start moving significantly slower than light and w will drop below 1/3. However, when it cools off further almost all of those particles annihilate and w rises up again.

This is my best understanding of how w changes:

At the end of inflation (during which w ~ -1) we get reheating. The temperature, T, is in the range of 10^22 eV. No elementary particles 173 GeV < m <~ 10^25 eV are known to exist (unless dark matter WIMPS are in this mass range). All the particle we know about have much less rest mass than T, so they are ultra-relativistic and w is very close to 1/3.

When T drops to ~173 GeV top quarks are no longer ultra-relativistic and w drops. Other particles are soon to follow. As the temperature drops quarks become less and less free.

When T drops below ~100 MeV quarks of any kind get rare. This is because the lightest isolatable particle with quarks is the pion at 135 and 140 MeV. No free quarks are known to exist, so the small mass of up and down quarks is irrelevant. Muons (m = 105MeV) also get rare around this point. Thus w increases to nearly 1/3.

When T nears ~500 keV electrons and positrons are no longer ultra-relativistic and w drops again. But when T gets lower they annihilate and w rises.

When T ~ 3eV ~ 30000K, the tiny amount of matter left over becomes dominant and w trends to zero (which just happens to be at 3eV). Note that this is a while before recombination occurs (T 0.3eV ~ 3000K). Even without baryon and WIMP asymmetry, neutrino masses are ~eV range (neutrinos interact too weakly to annihilate at the low densities in this era) so they would drive down w to zero around this time. The radiation era is over and it will be a long time before dark energy starts to matter.

Is my reasoning correct?

• As far as I know there is no "general w". Each particle type has its own $w$. So I dont think you can talk about for $w$ going up and down. Of course it decreases once a particle becomes non-relativistic but other then that it does not change – Layla Oct 21 '20 at 21:33
• @Layla: I mean the average w of all matter and energy at a given time. – Kevin Kostlan Oct 22 '20 at 6:21
• I see your point. I have some ideas but I am not sure they are true or not so Idk – Layla Oct 22 '20 at 11:12