The Dark Matter equation of state through cosmic history
  Cold Dark Matter (CDM) is a crucial constituent of the current concordance
cosmological model. Having a vanishing equation of state (EoS), its energy
density scales with the inverse cosmic volume and is thus uniquely described by
a single number, its present abundance. We test the inverse cosmic volume law
for Dark Matter (DM) by allowing its EoS to vary independently in eight
redshift bins in the range $z=10^5$ and $z=0$. We use the latest measurements
of the Cosmic Microwave Background radiation from the Planck satellite and
supplement them with Baryon Acoustic Oscillation (BAO) data from the 6dF and
SDSS-III BOSS surveys, and with the Hubble Space Telescope (HST) key project
data. We find no evidence for nonzero EoS in any of the eight redshift bins.
With Planck data alone, the DM abundance is most strongly constrained around
matter-radiation equality $\omega^{\rm eq}_g = 0.1193^{+0.0036}_{-0.0035}$ (95%
c.l.), whereas its present day value is more weakly constrained $\omega^{(0)}_g
= 0.16^{+0.12}_{-0.10}$ (95% c.l.). Adding BAO or HST data does not
significantly change the $\omega^{\rm eq}_g$ constraint, while $\omega^{(0)}_g$
tightens to $0.160^{+0.069}_{-0.065} $ (95% c.l.) and $0.124^{+0.081}_{-0.067}$
(95% c.l.) respectively. Our results constrain for the first time the level of
"coldness" required of the DM across various cosmological epochs and show that
the DM abundance is strictly positive at all times.
