An Exact Calculation of the Energy Density of Cosmological Gravitational Waves

TL;DR

This paper provides an exact calculation of the energy density of cosmological gravitational waves across different universe phases, using a continuous formalism for Bogoliubov coefficients, and predicts a high frequency cutoff.

Contribution

It introduces a formalism that computes Bogoliubov coefficients as continuous functions of time for cosmological backgrounds, enabling precise energy density calculations.

Findings

Derived the energy density of gravitational waves during inflation, radiation, and matter domination.

Predicted a natural high frequency cutoff in the gravitational wave spectrum.

Provided a method to incorporate the equation of state during reheating into the spectrum calculation.

Abstract

In this paper we calculate the Bogoliubov coefficients and the energy density of the stochastic gravitational wave background for a universe that undergoes inflation followed by radiation domination and matter domination, using a formalism that gives the Bogoliubov coefficients as continous functions of time. By making a reasonable assumption for the equation of state during reheating, we obtain in a natural way the expected high frequency cutoff in the spectral energy density.