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

[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 ?

 

[PeterDonis]

I read

Where? Please give a specific reference.

 

[DoobleD]

Where? Please give a specific reference.

Sure :

• wikipedia here, here and here,
• some of the sources used by wikipedia :
• 1. Ryden B: "Introduction to Cosmology", pg. 196 Addison-Wesley 2003
  2. Allday, Jonathan (2002). Quarks, Leptons and the Big Bang. Taylor & Francis. p. 334. ISBN 978-0-7503-0806-9.
  3. Our Universe Part 6: Electroweak Epoch, Scientific Explorer
• Kolb and Turner (1998) book, p. 118,
• In a 1984 paper, Alan Guth says the GUT energy scale is around 10¹⁴ GeV, which corresponds to 10^-35 s after the Big Bang (the paper is accessible here on p. 38),
• http://www.nicadd.niu.edu/~bterzic/PHYS652/Lecture_13.pdf, p. 67 and 69

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

<Moderator's note: Link changed due to possible copyright violation>

 

[George Jones]

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 ?

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 $g_* \approx 10$.

Where? Please give a specific reference.

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.

 

[DoobleD]

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 tGUTtGUTt_\rm{GUT} for TGUT≈1015 GeVTGUT≈1015 GeVT_\rm{GUT} \approx 10^{15} ~\rm{GeV} and g∗≈10g∗≈10g_* \approx 10.

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 ?

 

[George Jones]

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.

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.

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

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.

 

[DoobleD]

We are only looking at order of magnitude stuff. Even so, this is probably too small by an order of magnitude or so, since TGUT≈1015 GeVTGUT≈1015 GeVT_\rm{GUT} \approx 10^{15} ~\rm{GeV} or TGUT≈1016 GeVTGUT≈1016 GeVT_\rm{GUT} \approx 10^{16} ~\rm{GeV} for the Minimal Supersymmetric Standard Model (MSSM), which has loads of particle species.

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

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 tGUTtGUTt_\rm{GUT}, "Introduction to General Relativity" by Lewis Ryder.

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