Primordial Black Holes and Cosmological Phase Transitions Report ...

PBHs and Cosmological Phase Transitions 60
Figure 13: Schematic phase transition behaviour of Nf = 2 + 1 flavour QCD for
different choices of quark masses (mu,d and ms), at vanishing chemical potential
(µ = 0) (adapted from Laermann & Philipsen, 2003).
order transition, bounded by a second–order line as in Figure 13 (Forcrand &
Philipsen, 2006).
The critical temperature Tc is one of the most fundamental quantities in
QCD thermodynamics and is important in phenomenological studies of heavy–
ion collisions. Recently, several groups have tried to determine Tc near the
physical mass parameter in 2 + 1 flavour QCD by simulations with improved
staggered quarks (i.e. including fermionic fields in LGT). According to the
results obtained, a tentative conclusion is that the critical temperature in the
chiral limit is in the range 164 MeV − 186 MeV. In order to improve the results
further, simulations at lighter quark masses are necessary (Ejiri, 2007).
In Figure 14 we have a naive phase diagram of strongly interacting matter
in the T − n plane (n is the baryon density) where we consider Tc = 170 MeV.
Besides the radiation fluid, we might have as second fluid at the QCD epoch
the CDM: kinetically coupled (made up of neutralinos) and kinetically decoupled
(made up of axions and preexisting PBHs). Although CDM represents a major
component of the present Universe this was not the case at the QCD scale. In
fact, at that epoch we have (e.g. Schmid et al., 1999; Boyanovsky et al., 2006)
ρ CDM (Tc) ∼ 10 −8 ρ RAD (Tc) (111)
which means that the gravity generated by CDM can be neglected (e.g. Boyanovsky
et al., 2006).
In a first–order phase transition the QGP supercools until hadronic bubbles
are formed at some temperature Tsc ≈ 0.95Tc (e.g. Hwang, 2007). The crucial
parameters for supercooling are the surface tension σ (i.e. the work that has to
be done per unit area to change the phase interface at fixed volume) and the