On thermal gravitational contribution to particle production and dark matter

We investigate the particle production from thermal gravitational annihilation in the very early universe, which is an important contribution for particles that might not be in thermal equilibrium or/and might only have gravitational interaction, such as dark matter (DM). For particles with spin 0,1/2 and 1 we calculate the relevant cross sections through gravitational annihilation and give the analytic formulas with full mass-dependent terms. We find that DM with mass between TeV and 1016GeV could have the relic abundance that fits the observation, with small dependence on its spin. We also discuss the effects of gravitational annihilation from inflatons. Interestingly, contributions from inflatons could be dominant and have the same power dependence on Hubble parameter of inflation as that from vacuum fluctuation. Also, fermion production from inflaton, in comparison to boson, is suppressed by its mass due to helicity selection.