  We investigate the co-evolution of dark matter (DM) density perturbation and
metric perturbation in the WIMP paradigm. Instead of adopting the conventional
assumption that DM starts out in thermal equilibrium, we propose a simple phase
of DM production for the WIMP paradigm and extend our analysis to this phase.
Being free from the envelop of thermal equilibrium, an amplified perturbative
resonance between DM density perturbation and scalar modes of metric
perturbation takes place during the DM production phase, and consequently
results in a suppression of the tensor-to-scalar ratio of metric perturbation.
By specifying the cosmic background with a typical realization of cosmic
reheating, we establish a relation between DM particle mass $m_\chi$ and the
tensor-to-scalar ratio $r$ in the WIMP paradigm, which also contains two
reheating parameters, the reheating temperature $T_{R_f}$ and the dissipative
constant $\Gamma_0$. Notably, for a sizeable parameter region of WIMP candidate
and cosmic reheating, this relation predicts a smaller value of $r$ in
comparing with the conventional expectation obtained by assuming DM starts out
in thermal equilibrium. Once the suppression of $r$ is measured in future
observations of primordial gravitational wave in CMB, this relation can be used
to constrain $m_\chi$, $T_{R_f}$ and $\Gamma_0$ in principle.
