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 \(N_{\rm eff}\) parameter. The current theoretical uncertainty \(\Delta N_{\rm eff} \le 10^{-3}\) corresponds to \(T_{\rm max} \le 2\times 10^{17}\) 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.