Inflaton Production of Scalar Dark Matter through Fluctuations and Scattering

We study the effects on particle production of a Planck-suppressed coupling between the inflaton and a scalar dark matter candidate, $\chi$. In the absence of this coupling, the dominant source for the relic density of $\chi$ is the long wavelength modes produced from the scalar field fluctuations during inflation. In this case, there are strong constraints on the mass of the scalar and the reheating temperature after inflation from the present-day relic density of $\chi$ (assuming $\chi$ is stable). When a coupling $\sigma \phi^2 \chi^2$ is introduced, with $\sigma = {\tilde \sigma} m_\phi^2/ M_P^2 \sim 10^{-10} {\tilde \sigma}$, where $m_\phi$ is the inflaton mass, the allowed parameter space begins to open up considerably even for ${\tilde \sigma}$ as small as $\gtrsim 10^{-7}$. For ${\tilde \sigma} \gtrsim \frac{9}{16}$, particle production is dominated by the scattering of the inflaton condensate, either through single graviton exchange or the contact interaction between $\phi$ and $\chi$. In this regime, the range of allowed masses and reheating temperatures is maximal. For $0.004 < {\tilde \sigma} < 50$, constraints from isocurvature fluctuations are satisfied, and the production from parametric resonance can be neglected.