Primordial Black Holes and Cosmological Phase Transitions Report ...

PBHs and Cosmological Phase Transitions 66
transformation (see Schmid et al., 1999, for more details).
The expansion of the Universe is very slow compared to the strong, electromagnetic
and weak interactions around Tc. Thus, leptons, photons and the
QGP/HG are in thermal and chemical equilibrium at cosmological time scales.
All components have the same temperature locally, i.e., smeared over scales of
∼ 10 −7 RH. At larger scales, strongly, weakly and electromagnetically interacting
matter makes up a single perfect (i.e. dissipationless) radiation fluid (e.g.
Schmid et al., 1999).
In the case of a Crossover, instead of a first–order phase transition, the
sound speed decreases but does not vanish completely (e.g. Kämpfer, 2000). If
the Crossover is smooth, then no out–of–equilibrium aspects are expected as
the system will evolve in LTE (e.g. Boyanovsky et al., 2006).
If there is some cosmic dirt in the Universe such as PBHs, monopoles, strings,
and other kinds of defects, then the typical nucleation distance may differ significantly
from the scenario of homogeneous nucleation. That is because, in a
first–order phase transition, the presence of impurities lowers the energy barrier
and, thereby, the maximum amount of superccoling achieved during the
transition (Christiansen & Madsen, 1996).
A sketch of inhomogeneous bubble nucleation is shown in Figure 19. The
basic idea is that temperature inhomogeneities determine the location of bubble
nucleation. In cold regions, bubbles nucleate first. However, if the mean distance
between bubbles (∆nuc) is larger than the amplitude of the fluctuations δrms,
then the temperature inhomogeneities are negligible and the phase transition
proceeds via homogeneous nucleation (Boyanovsky et al., 2006).
2.2 Signatures of the QCD transition
A strong first–order QCD phase transition could lead to observable signatures
today. That is because, during phase coexistence, the Universe is effectively
unstable to gravitational collapse for all scales exceeding the mean distance
between hadron or quark–hadron bubbles (e.g. Jedamzik, 1998).
There are two kinds of effects emerging from the cosmological QCD phase
transition: the ones that affect scales λ ≤ dnuc (e.g. formation of quark nuggets,
generation of isothermal baryon fluctuations, generation of magnetic fields and
gravitational waves) and the ones that affect scales λ ≤ RH (e.g. formation
of CDM clumps, modification of primordial gravitational waves, formation of
PBHs).
As the first–order phase transition weakens, these effects become less pronounced.
Recent results provide strong evidence that the QCD transition is a
Crossover (cf. Section 2.3.3) and thus the above scenarios (and many others),
which arise from a strong first–order phase transition, are ruled out (e.g. Aoki
et al., 2006b). Bearing this in mind, we briefly describe some of the mentioned
QCD signatures.