New Constraints on Dark Matter Production during Kination

Our ignorance of the period between the end of inflation and the beginning of Big Bang Nucleosynthesis limits our understanding of the origins and evolution of dark matter. One possibility is that the Universe's energy density was dominated by a fast-rolling scalar field while the radiation bath was hot enough to thermally produce dark matter. We investigate the evolution of the dark matter density and derive analytic expressions for the dark matter relic abundance generated during such a period of kination. Kination scenarios in which dark matter does not reach thermal equilibrium require $\langle \sigma v \rangle < 2.7\times 10^{-38} \,\mathrm{cm^3\,s^{-1}}$ to generate the observed dark matter density while allowing the Universe to become radiation dominated by a temperature of $3 \, \mathrm{MeV}$. Kination scenarios in which dark matter does reach thermal equilibrium require $\langle \sigma v \rangle > 3\times 10^{-26} \,\mathrm{cm^3\,s^{-1}}$ in order to generate the observed dark matter abundance. We use observations of dwarf spheroidal galaxies by the Fermi Gamma-Ray Telescope and observations of the Galactic Center by the High Energy Stereoscopic System to constrain these kination scenarios. Combining the unitarity constraint on $\langle \sigma v \rangle$ with these observational constraints sets a lower limit on the temperature at which the Universe can become radiation dominated following a period of kination if ${\langle \sigma v \rangle > 3\times 10^{-31} \,\mathrm{cm^3\,s^{-1}}}$. This lower limit is between ${0.05 \, \mathrm{GeV}}$ and ${1 \, \mathrm{GeV}}$, depending on the dark matter annihilation channel.