Dark Matter Equation of State through Cosmic History

Cold dark matter 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 ω_{g}^{eq}=0.1193_{-0.0035}^{+0.0036} (95% C.L.), whereas its present-day value is more weakly constrained: ω_{g}^{(0)}=0.16_{-0.10}^{+0.12} (95% C.L.). Adding BAO or HST data does not significantly change the ω_{g}^{eq} constraint, while ω_{g}^{(0)} tightens to 0.160_{-0.065}^{+0.069} (95% C.L.) and 0.124_{-0.067}^{+0.081} (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.