Perturbative Resonance during Dark Matter Production and Its Cosmological Implications

Abstract

To trace the particle nature of dark matter (DM) from cosmic microwave background observations, we study the co-evolution of DM density perturbation and primordial metric perturbation during DM production. Solving the perturbative Einstein and Boltzmann equations, we unveil an amplified perturbative resonance between the DM density perturbation and the scalar modes of metric perturbation, driven by DM production. Such perturbative resonance does not affect the tensor modes and suppresses the tensor-to-scalar ratio of metric perturbation $r$. Using a typical model to specify cosmic reheating, we obtain a direct relation between DM particle mass $m_\chi$ and $r$, which can constrain $m_\chi$ in future primordial gravitational wave searches.