Primordial Black Holes and Cosmological Phase Transitions Report ...

PBHs and Cosmological Phase Transitions 68
Isothermal baryon fluctuations
The large isothermal baryon fluctuations, induced during the separation of
phases, could lead to inhomogeneous initial conditions for nucleosynthesis. The
requirement is that dnuc must be greater than the proton diffusion length which
is ∼ 3 m at the QCD epoch. This is more than 10 2 times larger than the dnuc
value based on lattice results (e.g. Boyanovsky et al., 2006; Schmid et al., 1999).
Gravitational waves
In principle, primordial gravitational waves (e.g. from cosmological inflation)
present a clean probe of the dynamics of the early Universe, since they know
only about the Hubble expansion (e.g. Boyanovsky et al., 2006). The dramatic
drop in relativistic degrees of freedom during the QCD phase transition (see
Section 1.10) induces a jump of 30% in the primordial spectrum of gravitational
waves. Today this jump might be, in principle, observed at ∼ 10 −8 Hz for pulsar
timing (e.g. Boyanovsky et al., 2006).
In Figure 20 we show the energy density, per logarithmic frequency interval
Ωgw, for primordial gravitational waves from the QCD transition. The length
scales that cross into the horizon after the transition (left hand side of Figure 20)
are unaffected, whereas modes that cross the horizon before the transition are
damped by an additional factor ≈ 0.7. The modification of the differential
spectrum has been calculated for a first–order Bag Model and a Crossover QCD
transition. In both cases the step extends over one decade in frequency. Notice
that the detailed form of the jump is almost independent from the order of
the transition (e.g. Boyanovsky et al., 2006). In Figure 20 it is also indicated
the frequency range in which limits on Ωgw have been reported from pulsar
timing residuals. Unfortunately, todays technology does not enable us to detect
primordial gravitational waves at frequencies around 10 −7 Hz, because their
expected amplitude is too small (e.g. Boyanovsky et al., 2006).
QCD balls
If axions existed and if the reheating scale after inflation is above the Peccei-
Quinn 26 scale, collapsing axion domain walls could trap a large number of
quarks. At some point the collapse would be stopped by the Fermi pressure
of the quarks, which would then settle in a colour superconducting phase. This
process takes place during the QCD transition, but does not require a first–order
transition, contrary to the idea of strange quark nuggets (e.g. Schwarz, 2003).
2.3 QCD models
There are three main models often used in the study of the QCD transition: the
Bag Model, the Lattice Fit and the Crossover. Although recent results provide
26 In particle physics, the Peccei–Quinn theory is, perhaps, one of the most famous proposed
solution to the Strong CP problem (the puzzling question: why QCD does not seem to break
the CP–symmetry?), involving hypothetical particles called axions.