Testing the warmness of dark matter

Dark matter (DM) as a pressureless perfect fluid provides a good fit of the standard $\Lambda$CDM model to the astrophysical and cosmological data. In this paper, we investigate two extended properties of DM: a possible time dependence of the equation of state of DM via Chevallier-Polarski-Linder parametrization, $w_{\rm dm} = w_{\rm dm 0} + w_{\rm dm 1}(1-a)$, and the constant non-null sound speed $\hat{c}^2_{\rm s,dm}$. We analyze these DM properties on top of the base $\Lambda$CDM model by using the data from Planck cosmic microwave background (CMB) temperature and polarization anisotropy, baryonic acoustic oscillations (BAO) and the local value of the Hubble constant from the Hubble Space Telescope (HST). We find new and robust constraints on the extended free parameters of DM. The most tight constraints are imposed by CMB + BAO data where the three parameters $w_{\rm dm0}$, $w_{\rm dm1}$ and $\hat{c}^2_{\rm s,dm}$ are respectively constrained to be less than $1.43\times 10^{-3}$, $1.44\times 10^{-3}$ and $1.79\times 10^{-6}$ at 95\% CL. All the extended parameters of DM show consistency with zero at 95\% CL, indicating no evidence beyond the CDM paradigm. We notice that the extended properties of DM significantly affect several parameters of the base $\Lambda$CDM model. In particular, in all the analyses performed here, we find significantly larger mean values of $H_0$ and lower mean values of $\sigma_8$ in comparison to the base $\Lambda$CDM model. Thus, the well-known $H_0$ and $\sigma_8$ tensions might be reconciled in the presence of extended DM parameters within the $\Lambda$CDM framework. Also, we estimate the warmness of DM particles as well as its mass scale and find a lower bound: $\sim$ 500 eV from our analyses.