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We investigate the co-evolution of dark matter (DM) density perturbation andmetric perturbation in the WIMP paradigm. Instead of adopting the conventionalassumption that DM starts out in thermal equilibrium, we propose a simple phaseof DM production for the WIMP paradigm and extend our analysis to this phase.Being free from the envelop of thermal equilibrium, an amplified perturbativeresonance between DM density perturbation and scalar modes of metricperturbation takes place during the DM production phase, and consequentlyresults in a suppression of the tensor-to-scalar ratio of metric perturbation.By specifying the cosmic background with a typical realization of cosmicreheating, we establish a relation between DM particle mass $m_\chi$ and thetensor-to-scalar ratio $r$ in the WIMP paradigm, which also contains tworeheating parameters, the reheating temperature $T_{R_f}$ and the dissipativeconstant $\Gamma_0$. Notably, for a sizeable parameter region of WIMP candidateand cosmic reheating, this relation predicts a smaller value of $r$ incomparing with the conventional expectation obtained by assuming DM starts outin thermal equilibrium. Once the suppression of $r$ is measured in futureobservations of primordial gravitational wave in CMB, this relation can be usedto constrain $m_\chi$, $T_{R_f}$ and $\Gamma_0$ in principle.

Perturbative Resonance in WIMP paradigm and its Cosmological Implications on Cosmic Reheating and Primordial Gravitational Wave Detection