An upper limit on the initial temperature of the radiation-dominated Universe

Gravitational waves (GWs) are produced by colliding particles through the gravitational analogue of electromagnetic bremsstrahlung. We calculate the contribution of free-free emission in the radiation-dominated Universe to the stochastic GW background. We find that the energy density of the resulting GW radiation is heavily dependent on the number of elementary particles, Ntot, and the maximum initial temperature, Tmax. We rule out Ntot≳102×NSM for Tmax∼TPlanck≈1019 GeV and Ntot≳1016×NSM for Tmax∼1016 GeV, where NSM is the number of particles in the Standard Model. In the case of inflation, existing cosmological data constrain Tmax≲1016 GeV . However, alternative models to inflation such as bouncing cosmologies allow for Tmax near TPlanck. At the energy scales we are considering, the extra number of particles arise naturally in models of extra dimensions.