# I Why the GUT epoch ended at ~10^-36 s ?

1. Jul 26, 2017

### DoobleD

I read that the GUT epoch is estimated to have ended at around 10-36 s, but I can't find any proof or derivation for this. Anyone knows ?

2. Jul 26, 2017

### Staff: Mentor

Where? Please give a specific reference.

3. Jul 26, 2017

### DoobleD

Sure :
The list goes on, but I didn't find a source with a proof or at least some qualitative justification for this.

Last edited by a moderator: Jul 27, 2017
4. Jul 26, 2017

### George Jones

Staff Emeritus
Try using (3.2.68) of Daniel Baumann's (Cambridge) excellent cosmology lecture notes
http://www.damtp.cam.ac.uk/user/db275/Cosmology/Lectures.pdf
to find $t_\rm{GUT}$ for $T_\rm{GUT} \approx 10^{15} ~\rm{GeV}$ and $g_* \approx 10$.

Within one or two orders of magnitude, it is ubiquitous in the literature, e.g., on page 190 of the second edition of the often-used text "Introduction to Cosmology" by Barbara Ryden.

5. Jul 26, 2017

### DoobleD

Seems to be it, thank you ! I get, using $T_\rm{GUT} \approx 10^{15} ~\rm{GeV} = 10^{18} MeV$ :

$t \approx \frac{9}{4\sqrt{10}T^2} \approx 7 \times 10^{-37} s$, which is close enough.

One thing I'm not sure about though is why the choice of $g_* \approx 10$ degrees of freedom ?

6. Jul 26, 2017

### George Jones

Staff Emeritus
I have a few books that give expressions equivalent to Baumann's (3.2.68), but, as far as I can see, I have only one book that explicitly uses this expression to estimate $t_\rm{GUT}$, "Introduction to General Relativity" by Lewis Ryder.

We are only looking at order of magnitude stuff. Even so, this is probably too small by an order of magnitude or so, since $T_\rm{GUT} \approx 10^{15} ~\rm{GeV}$ or $T_\rm{GUT} \approx 10^{16} ~\rm{GeV}$ for the Minimal Supersymmetric Standard Model (MSSM), which has loads of particle species.

7. Jul 27, 2017

### DoobleD

Right, $g_*$ doesn't change much the estimation anyway. I was just curious of what those degrees mean, but doesn't really matter.

Thanks, I got the book and found it indeed, on page 384. I'll keep those two references.