Precision calculations of the gravitational wave background spectrum from inflation

Abstract

The spectrum of the gravitational wave background originating from quantum fluctuations during inflation is calculated numerically for various inflation models over a wide range of frequencies. We take into account four ingredients: the scalar field dynamics during inflation making no use of the slow-roll approximation, the fermionic decay of the scalar field with a small coupling constant during the reheating process, the change of the effective number of degrees of freedom ${g}_{*}$ in the radiation-dominated era, and the anisotropic stress of free-streaming neutrinos. By numerically solving the evolution of gravitational waves during and after inflation up to the present, all of these effects can be examined comprehensively and accurately over a broad spectrum, even at very high frequencies. We find that the spectrum shows (i) a large deviation from the spectrum less accurate obtained by Taylor expanding around the CMB scale using the slow-roll approximation, (ii) a characteristic frequency dependence due to the reheating effect, and (iii) damping due to the ${g}_{*}$ changes and the neutrino anisotropic stress. We suggest that future analysis of the gravitational wave background should take into consideration the fact that analytical estimates using the Taylor expansion overestimate the amplitude of the spectrum.