  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.
