Gravitational wave background from Standard Model physics: Complete leading order

Abstract

We compute the production rate of the energy density carried by gravitational waves emitted by a Standard Model plasma in thermal equilibrium, consistently to leading order in coupling constants for momenta $k\sim \pi T$. Summing up the contributions from the full history of the universe, the highest temperature of the radiation epoch can be constrained by the so-called $N_{\mathrm{eff}}$ parameter. The current theoretical uncertainty $\Delta N_{\mathrm{eff}}\le 10^{-3}$ corresponds to $T_{\max }\le 2\times 10^{17}$ GeV. In the course of the computation, we show how a subpart of the production rate can be determined with the help of standard packages, even if subsequently an IR subtraction and thermal resummation need to be implemented.

Comments: 33 pages. v2: clarifications and an ancillary data file added