Primordial Black Holes and Cosmological Phase Transitions Report ...

PBHs and Cosmological Phase Transitions 70
Figure 21: The behaviour of the sound speed (equation 14) during the QCD
transition as a function of the scale factor R (adapted from Schwarz, 2003).
During a first–order transition (Lattice Fit and Bag Model) the sound speed
vanishes, suddenly rising, at the end of the transition (R = R+), to the original
value 1/ √ 3.
different regions: a high temperature region (T > Tc) where we have a gas of
massless quarks and gluons (QGP) and a low temperature region (T < Tc) where
we have a gas of free massless pions (HG). At T = Tc quarks, gluons and pions
coexist in equilibrium at constant pressure and temperature (e.g. Boyanovsky
et al., 2006).
The pressure for the high temperature region, which corresponds to a QGP
is given, for vanishing chemical potential (µ = 0), by (e.g. Schmid et al., 1999)
pQGP (T )=p ideal
QGP (T ) − B (123)
where we have, considering that gluons and existing quarks are effectively massless
at T ≈ Tc, that (e.g. Schmid et al., 1999)
p ideal
QGP (T )= π2
90 gQGP T 4
(124)
where gQGP corresponds to the number of degrees of freedom of the QGP at
the beginning of the transition (see Section 1.10). The low temperature region,
which corresponds to an HG, can be modeled as a gas of massless pions with
(e.g. Schmid et al., 1999)
pHG(T )= π2 4
gHGT
90
(125)
where gHG represents the number of degrees of freedom of the HG at the end
of the transition (see Section 1.10).