  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 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 $10^{16}$GeV 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 inflatons, in comparison to boson,
is suppressed by its mass due to helicity selection.
