  An era of kination occurs when the Universe's energy density is dominated by
a fast-rolling scalar field. Dark matter that is thermally produced during an
era of kination requires larger-than-canonical annihilation cross sections to
generate the observed dark matter relic abundance. Furthermore, dark matter
density perturbations that enter the horizon during an era of kination grow
linearly with the scale factor prior to radiation domination. We show how the
resulting enhancement to the small-scale matter power spectrum increases the
microhalo abundance and boosts the dark matter annihilation rate. We then use
gamma-ray observations to constrain thermal dark matter production during
kination. The annihilation boost factor depends on the minimum halo mass, which
is determined by the small-scale cutoff in the matter power spectrum.
Therefore, observational limits on the dark matter annihilation rate imply a
minimum cutoff scale for a given dark matter particle mass and kination
scenario. For dark matter that was once in thermal equilibrium with the
Standard Model, this constraint establishes a maximum allowed kinetic
decoupling temperature for the dark matter. This bound on the decoupling
temperature implies that the growth of perturbations during kination cannot
appreciably boost the dark matter annihilation rate if dark matter was once in
thermal equilibrium with the Standard Model.
