Cosmological searches for a non-cold dark matter component

We explore an extended cosmological scenario where the dark matter is an admixture of cold and additional non-cold species. The mass and temperature of the non-cold dark matter particles are extracted from a number of cosmological measurements. Among others, we consider tomographic weak lensing data and Milky Way dwarf satellite galaxy counts. We also study the potential of these scenarios in alleviating the existing tensions between local measurements and Cosmic Microwave Background (CMB) estimates of the $S_8$ parameter, with $S_8=\sigma_8\sqrt{\Omega_m}$, and of the Hubble constant $H_0$. In principle, a sub-dominant, non-cold dark matter particle with a mass $m_X\sim$~keV, could achieve the goals above. However, the preferred ranges for its temperature and its mass are different when extracted from weak lensing observations and from Milky Way dwarf satellite galaxy counts, since these two measurements require suppressions of the matter power spectrum at different scales. Therefore, solving simultaneously the CMB-weak lensing tensions and the small scale crisis in the standard cold dark matter picture via only one non-cold dark matter component seems to be challenging.