  We calculate the relaxation rate of a scalar field in a plasma of other
scalars and fermions with gauge interactions using thermal quantum field
theory. It yields the rate of cosmic reheating and thereby determines the
temperature of the "hot big bang" in inflationary cosmology. The total rate
originates from various processes, including decays and inverse decays as well
as Landau damping by scatterings. It involves quantum statistical effects and
off-shell transport. Its temperature dependence can be highly nontrivial,
making it impossible to express the reheating temperature in terms of the model
parameters in a simple way. We pay special attention to the temperature
dependence of the phase space due to the modified dispersion relations in the
plasma. We find that it can have a drastic effect on the efficiency of
perturbative reheating, which depends on the way particles in the primordial
plasma interact. For some interactions thermal masses can effectively close the
phase space for the dominant dissipative processes and thereby impose an upper
bound on the reheating temperature. In other cases they open up new channels of
dissipation, hence increase the reheating temperature. At high temperatures we
find that the universe can even be heated through couplings to fermions, which
are often assumed to be negligible due to Pauli-blocking. These effects may
also be relevant for baryogenesis, dark matter production, the fate of moduli
and in scenarios of warm inflation.
