Improved calculation of relic gravitational waves

Abstract

In this paper, we improve the calculation of the relic gravitational waves (RGW) in two aspects: First, we investigate the transfer function after considering the redshift-suppression effect, the accelerating expansion effect, the damping effect of free-streaming relativistic particles, and the damping effect of cosmic phase transition, and give a simple approximate analytic expression, which clearly illustrates the dependent relations on the cosmological parameters. Second, we develop a numerical method to calculate the primordial power spectrum of RGW at a very wide frequency range, where the observed constraints on $n_s$ (the scalar spectral index) and $P_S(k_0)$ (the amplitude of primordial scalar spectrum) and the Hamilton-Jacobi equation are used. This method is applied to two kinds of inflationary models, which all satisfy the current constraints on $n_s$, $α$ (the running of $n_s$) and $r$ (the tensor-scalar ratio). We plot them in the $r-Ω_g$ diagram, where $Ω_g$ is the strength of RGW, and study their detection by the CMB experiments and laser interferometers.