Improved Calculation of the Primordial Gravitational Wave Spectrum in the Standard Model

We show that the energy density spectrum of the primordial gravitational waves has characteristic features due to the successive changes in the relativistic degrees of freedom during the radiation era. These changes make the evolution of radiation energy density deviate from the conventional adiabatic evolution, rho_r~ a^{-4}, and thus cause the expansion rate of the universe to change suddenly at each transition which, in turn, modifies the spectrum of primordial gravitational waves. We take into account all the particles in the Standard Model of elementary particles. In addition, free-streaming of neutrinos damps the amplitude of gravitational waves, leaving characteristic features in the energy density spectrum. Our calculations are solely based on the standard model of cosmology and particle physics, and therefore these features must exist. Our calculations significantly improve the previous ones which ignored these effects and predicted a smooth, featureless spectrum.