Primordial Black Holes and Cosmological Phase Transitions Report ...

PBHs and Cosmological Phase Transitions 19
into quanta of many other fields, which, through scattering processes, reach a
state of local thermodynamic equilibrium. This period is followed by deccelerated
expansion and cooling, with the Universe successively visiting the different
energy scales at which particle and nuclear physics predict symmetry breaking
phase transitions. Those phase transitions are broadly characterized as either
second or first–order (e.g. Boyanovsky et al., 2006).
If a thermodynamic quantity changes discontinuously (for example as a function
of temperature) we have a first–order phase transition. This happens because,
at the point at which the transition occurs, there are two separate thermodynamic
states in equilibrium. Any thermodynamic quantity that undergoes
such a discontinuous change at the phase transition is referred to as an order
parameter. Whether or not a first–order phase transition occurs often depends
on other parameters that enter the theory. It is possible that, while another
parameter is varied, the change in the order parameter of the phase transition
decreases until they, together with all other thermodynamic quantities, become
continuous at the transition point. In this case we refer to a second order phase
transition at the point at which the transition becomes continuous (i.e., it shows
a thermodynamic behaviour without discontinuities or singularities in the free
energy or any of its derivatives), and a continuous crossover at the other points
for which all physical quantities undergo no changes (e.g. Trodden, 1999). However,
if the crossover is relatively sharp the situation may not be too different
from a phase transition (e.g. Boyanovsky et al., 2006).
Phase transitions are the most important phenomena in particle cosmology
since, without them, the history of the Universe would simply be one of gradual
cooling. In the absence of phase transitions, the only departure from thermal
equilibrium is provided by the expansion of the Universe (e.g. Trodden, 1999).
The SMPP (Section 1.8) predicts two phase transitions. The first one, at
temperatures of ∼ 100 GeV, is the Electroweak phase transition (Section 3)
which was responsible for the spontaneous breaking of the EW symmetry, which
gives the masses to the elementary particles. This transition is also related to
the EW baryon–number violating processes, which had a major influence on the
observed baryon–asymmetry of the Universe (e.g. Aoki et al., 2006b).
The second transition occurs at T ≈ 170 MeV. It is related to the spontaneous
breaking of the chiral symmetry of the Quantum Chromodynamics (QCD)
when quarks and gluons become confined in hadrons (Section 2). At high temperatures
asymptotic freedom of QCD predicts the existence of a deconfined
phase (according to lattice QCD simulations), the Quark–Gluon Plasma (QGP).
At low temperatures quarks and gluons are confined in a Hadron Gas (HG) (e.g.
Schmid et al., 1999).
The QCD phase transition was pointed out, for a long time, as a prime candidate
for a first–order phase transition (e.g. Jedamzik & Niemeyer, 1999). Recent
results (e.g. Aoki et al., 2006b) provide strong evidence that the QCD transition
is a simple Crossover instead. Here we will consider the two possibilities (see
Section 2).