Gravitational wave background from Standard Model physics: complete leading order

A bstract 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 ∼ πT . 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 eff parameter. The current theoretical uncertainty ∆ N eff ≤ 10 − 3 corresponds to T max ≤ 2 × 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.