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.
