Primordial Black Holes and Cosmological Phase Transitions Report ...

PBHs and Cosmological Phase Transitions 72
Figure 22: The entropy density of hot QCD relative to the entropy density of an
ideal QGP for the Lattice Fit QCD data (Nf = 0 and Nf = 2 quark flavours),
Bag Model, and for a smooth Crossover (adapted from Schmid et al., 1999).
It is useful to write a single expression for the entropy on the Bag Model as
(Schwarz, 1998)
s(T )= 2π2
3
gHGT 1+
45 ∆g
Θ(T − Tc)
(135)
gHG
where ∆g = gQGP − gHG and the function Θ is defined as (Schwarz, 1998)
0
Θ(T − Tc) =
1
if T < Tc
if T > Tc
(136)
The typical value for the bag constant is given by B 1/4 ∼ 200 MeV (e.g. Boyanovsky
et al., 2006). Inserting B 1/4 = 200 MeV into equation (134) one gets,
considering two quark flavours (gQGP = 51.25, cf. Section 1.10) and three massless
pions (gHG = 17.25, cf. Section 1.10), that Tc ≈ 145 MeV, which is not too
far from the lattice result Tc ∼ 170 MeV (e.g. Boyanovsky et al., 2006, Section
2.3.2).
In the Bag Model the sound speed stays at c 2 s =1/3 before and after the
transition and vanishes during the transition (e.g. Schwarz, 2003) as can be
inferred from Figure 21.
2.3.2 Lattice Fit
Lattice Gauge Theory (LGT) is the study of Gauge Theories on a space–time
that as been discretized onto a lattice. One hopes that performing simulations
on larger and larger lattices, while making the lattice spacing, a, smaller and
smaller, the behaviour of the continuum theory can be recovered. In the case of