Primordial Black Holes and Cosmological Phase Transitions Report ...

PBHs and Cosmological Phase Transitions 53
tion 104) giving (e.g. Ignatius, 1993)
g(T )=gγ + g W ± ,Z 0 + gg + gH + 7
8 [ ge,µ,τ + gν + gq ]=
2+3× 2+8× 2 + 4 + 7
8 [3 × 4+3× 2+6× 12] = 106.75.
(106)
As the expansion of the Universe goes on, the temperature decreases and it will
equal, successively, the threshold of each particle leading to smaller values of
g(T ). This evolution is represented on Table 13 where we have, in the first row,
the case when all the particles are present and, on the final row, the present day
case with only neutrinos and photons.
At temperatures above 1 MeV, electrons, photons and neutrinos have the
same temperature. Below this temperature the three neutrino flavours are decoupled
chemically and kinetically from the radiation plasma. This early decoupling
from thermal evolution with the rest of the Universe is due to the fact that
neutrinos interact with other particles only via weak interactions (e.g. Gynther,
2006). As a result, the entropy of the relativistic electrons is transferred to the
photon entropy, but not to the neutrino entropy when electrons and positrons
annihilate. This leads to an increase of the photon temperature relative to the
neutrino temperature by (e.g Schwarz, 2003)
Tν =
1/3 4
Tγ. (107)
11
As a result, below T ∼ 1 MeV we have to consider the effective number of
degrees of freedom of the energy density, gρ, and the number of degrees of
freedom of the entropy density, gs (e.g Schwarz, 2003). The present value of gρ
is (e.g. Coleman & Ross, 2003)
gρ(T )=gγ +6× 7
4/3 4
≈ 3.363. (108)
8 11
On the other hand we have gs(T ) ≈ 3.909 at the present (e.g Schwarz, 2003).
At the temperature of the QCD transition (Tc ≈ 170 MeV, see Section 2)
the number of degrees of freedom changes very rapidly, since quarks and gluons
are coloured. Before the QCD transition we have g = 61.75 (or g = 51.25 not
including the strange quark) and after the transition we have g = 17.25 (cf.
Table 13) which gives ∆g ≈ 45. At still higher temperatures, heavier particles
are excited, but within the SMPP nothing so spectacular as the QCD transition
happens. Within the SMPP the EW transition is only a tiny effect (e.g. Schwarz,
2003) with ∆g = 96.25 − 95.25 = 1.
This situation is drastically changed if one considers the MSSM (see Section
1.9). On Table 14 we list the contribution that each particle and each sparticle
species might give to g(T ). Note that the contributions from squarks, sleptons
and gluinos is identical to that of, respectively, quarks, leptons and gluons
(apart from the factor 7/8). The Higgs sector now is formed by two doublets