Primordial Black Holes and Cosmological Phase Transitions Report ...

PBHs and Cosmological Phase Transitions 65
Figure 18: The Hubble rate H and the typical interaction rates of weak (Γw) and
electric (Γe) processes that involve relativistic particles, as well as the typical
rate of a weak annihilation rate Γw,ann for a particle mass of 100 GeV. The
dashed line indicates the rate 1/s. At tH ∼ 1s, the weak interaction rate falls
below the expansion rate (chemical and kinetic decoupling of neutrinos, kinetic
decoupling of neutralinos); at temperatures of the order of 1-10 GeV neutralinos
freeze–out. The electric interaction rate stays well above the Hubble rate up
to the epoch of photon decoupling, which occurs well after the epochs we show
here (Schwarz, 2003).
librium (LTE) depends on the comparison of two time scales: the cooling rate
due to cosmological expansion (e.g. Boyanovsky et al., 2006)
1 dT (t) 1 dR(t)
= − = −H(t) (122)
T (t) dt R(t) dt
and the rate of equilibration Γ. LTE follows when Γ >H(t), in which case the
evolution is adiabatic in the sense that the thermodynamic functions depend
slowly on time through the temperature (e.g. Boyanovsky et al., 2006, see Figure
18). Strong, electric, and weak interactions keep all relativistic particles in
kinetic and chemical equilibrium down to temperatures of ∼ 1 MeV. At that
point neutrinos and neutrons decouple chemically and kinetically from the rest
of the radiation fluid (e.g. Schwarz, 2003).
When the cosmological expansion is too fast (namely H(t) ≫ Γ) LTE cannot
happen, the temperature drops too fast for the system to have time to relax to
LTE and the phase transition occurs via a quench from the high into the low
temperature phase (e.g. Boyanovsky et al., 2006).
In the case of the QCD transition the isentropic condition applies after initial
supercooling, bubble nucleation, and sudden reheating to Tc. During this part
of the transition, which takes about 99% of the transition time, the fluid is
extremely close to thermal equilibrium, because the time to reach equilibrium
is very much shorter than a Hubble time, i.e. the fluid makes a reversible