Improved calculation of relic gravitational waves

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 ns (the scalar spectral index) and PS(k0) (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 ns, α (the running of ns) and r (the tensor-scalar ratio). We plot them in the r − Ωg diagram, where Ωg is the strength of RGW, and study their detection by the CMB experiments and laser interferometers. PACC number: 0430, 9880