Improved calculation of relic gravitational waves

TL;DR

This paper enhances the calculation of relic gravitational waves by deriving an analytic transfer function considering various effects and developing a numerical method to evaluate the primordial spectrum across a wide frequency range, aiding detection efforts.

Contribution

It introduces a simple analytic transfer function considering multiple effects and a numerical method for wide-range primordial spectrum calculation, applied to inflationary models under current constraints.

Findings

Derived an analytic transfer function illustrating parameter dependencies.

Developed a numerical method for primordial spectrum over wide frequencies.

Analyzed detectability of RGW with CMB and interferometers.

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 $n_s$, $\alpha$ (the running of $n_s$) and $r$ (the tensor-scalar ratio). We plot them in the $r-\Omega_g$ diagram, where $\Omega_g$ is the strength of RGW, and study their detection by the CMB experiments and laser interferometers.