  In this paper, we investigate the possibility of testing the weakly
interacting massive particle (WIMP) dark matter (DM) models by applying the
simplest phenomenological model which introduces an interaction term between
dark energy (DE) and WIMP DM, i.e., $Q = 3\gamma_{DM} H\rho_{DM}$. In general,
the coupling strength $\gamma_{DE}$ is close to $0$ as the interaction between
DE and WIMP DM is very weak, thus the effect of $\gamma_ {DE}$ on the evolution
of $Y$ associated with DM energy density can be safely neglected. Meanwhile,
our numerical calculation also indicates that $x_f\approx20$ is associated with
DM freeze-out temperature, which is the same as the vanishing interaction
scenario. As for DM relic density, it will be magnified by
$\frac{2-3\gamma_{DM}}{2}[{2\pi g_* m_{DM}^3}/{(45 s_0 x_f^3})]^{\gamma_{DM}}$
times, which provides a new way to test WIMP DM models. As an example, we
analyze the case in which WIMP DM is a scalar DM. (SGL+SNe+Hz) and
(CMB+BAO+SNe) cosmological observations will give
$\gamma_{DM}=0.134^{+0.17}_{-0.069}$ and $\gamma_{DM}=-0.0008\pm0.0016$,
respectively. After further considering the constraints from DM direct
detection experiment, DM indirect detection experiment, and DM relic density,
we find that the allowed parameter space of the scalar DM model will be
completely excluded for the former cosmological observations, while it will
increase for the latter ones. Those two cosmological observations lead to an
almost paradoxical conclusion. Therefore, one could expect more stringent
constraints on the WMIP DM models, with the accumulation of more accurate
cosmological observations in the near future.
