Dark matter of weakly interacting massive particles and the QCD equation of state

Weakly Interacting Massive Particles (WIMPs) of mass $m$ freeze-out at a temperature $T_f\simeq m/25$, i.e. in the range 400 MeV–40 GeV for a particle in the typical mass range 10–1000 GeV. The WIMP relic density, which depends on the effective number of relativistic degrees of freedom at $T_f$, may be measured to better than $1\%$ by Planck, warranting comparable theoretical precision. Recent theoretical and experimental advances in the understanding of high-temperature QCD show that the quark gluon plasma departs significantly from ideal behavior up to temperatures of several GeV, necessitating an improvement of the cosmological equation of state over those currently used. We discuss how this increases the relic density by approximately 1.5–$3.5\%$ in benchmark mSUGRA models, with an uncertainty in the QCD corrections of 0.5–$1\%$. We point out what further work is required to achieve a theoretical accuracy comparable with the expected observational precision, and speculate that the effective number of degrees of freedom at $T_f$ may become measurable in the foreseeable future.

Figure 1

Degrees of freedom factors $g_{*}^{1/2}(T)$ and $h_{\mathrm{eff}}(T)$, defined in Eqs. (3, 5), for our equation of state B (solid) compared with those currently used in DarkSUSY and MicrOMEGAs (dashed). The spike in the upper panel is a numerical artefact without physical impact, see text.