An Exact Calculation of the Energy Density of Cosmological Gravitational   Waves
  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. 
L. E. Mendes, A. B. Henriques and R. G. Moorhouse