  In a broad class of theories, the relic abundance of dark matter is
determined by interactions internal to a thermalized dark sector, with no
direct involvement of the Standard Model (SM). We point out that these theories
raise an immediate cosmological question: how was the dark sector initially
populated in the early universe? Motivated in part by the difficulty of
accommodating large amounts of entropy carried in dark radiation with cosmic
microwave background measurements of the effective number of relativistic
species at recombination, $N_{\mathrm{eff}}$, we aim to establish which
admissible cosmological histories can populate a thermal dark sector that never
reaches thermal equilibrium with the SM. The minimal cosmological origin for
such a dark sector is asymmetric reheating, when the same mechanism that
populates the SM in the early universe also populates the dark sector at a
lower temperature. Here we demonstrate that the resulting inevitable
inflaton-mediated scattering between the dark sector and the SM can wash out a
would-be temperature asymmetry, and establish the regions of parameter space
where temperature asymmetries can be generated in minimal reheating scenarios.
Thus obtaining a temperature asymmetry of a given size either restricts
possible inflaton masses and couplings or necessitates a non-minimal cosmology
for one or both sectors. As a side benefit, we develop techniques for
evaluating collision terms in the relativistic Boltzmann equation when the full
dependence on Bose-Einstein or Fermi-Dirac phase space distributions must be
retained, and present several new results on relativistic thermal averages in
an appendix.
