Dark Matter properties through cosmic history

We perform the first test of dark matter (DM) stress-energy evolution through cosmic history, using cosmic microwave background measurements supplemented with baryon acoustic oscillation data and the Hubble Space Telescope key project data. We constrain the DM equation of state (EoS) in 8 redshift bins, and its sound speed and (shear) viscosity in 9 redshift bins, finding no convincing evidence for non-$\Lambda$CDM values in any of the redshift bins. Despite this enlarged parameter space, the sound speed and viscosity are constrained relatively well at late times (due to the inclusion of CMB lensing), whereas the EoS is most strongly constrained around recombination. These results constrain for the first time the level of "coldness" required of DM across various cosmological epochs at both the background and perturbative levels. We show that simultaneously allowing time dependence for both the EoS and sound speed parameters shifts the posterior of the DM abundance before recombination to a higher value, while keeping the present day DM abundance similar to the $\Lambda$CDM value. This shifts the posterior for the present day Hubble constant compared to $\Lambda$CDM, suggesting that DM with time-dependent parameters is well-suited to explore possible solutions to persistent tensions within the $\Lambda$CDM model. We perform a detailed comparison with our previous study involving a vanishing sound speed and viscosity using the same datasets in order to explain the physical mechanism behind these shifts.