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, N_tot, and the maximum initial temperature, T_max. We rule out N_tot ≳ 10² × N_SM for T_max ∼ T_Planck ≈ 10¹⁹ GeV and N_tot ≳ 10¹⁶ × N_SM for T_max ∼ 10¹⁶ GeV, where N_SM is the number of particles in the Standard Model. In the case of inflation, existing cosmological data constrain T_max ≲ 10¹⁶ GeV . However, alternative models to inflation such as bouncing cosmologies allow for T_max near T_Planck. At the energy scales we are considering, the extra number of particles arise naturally in models of extra dimensions.