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 $n_s$, $\alpha$ (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.

17 pages, 3 figures, minor typos corrected

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• Primordial backgrounds of relic gravitons
• Primordial Gravitational Waves Predictions for GW170817-compatible Einstein-Gauss-Bonnet Theory
• Chirality of Gravitational Waves in Chern-Simons $f(R)$ Gravity Cosmology
• Amplification of the Primordial Gravitational Waves Energy Spectrum by a Kinetic Scalar in $F(R)$ Gravity
• Amplification of Primordial Gravitational Waves by a Geometrically Driven non-canonical Reheating Era
• $f(R)$-Gravity Generated Post-inflationary Eras and their Effect on Primordial Gravitational Waves
• Reconstructing Dark Energy Potentials From Parameterized Deceleration Parameters
• Effects of a Pre-inflationary de Sitter Bounce on the Primordial Gravitational Waves in $f(R)$ Gravity Theories
• Detecting Relic Gravitational Waves in the CMB: Comparison of Planck and Ground-based Experiments
• Propagation of gravitational waves in an expanding background in the presence of a point mass
• Exact solutions of primordial gravitational waves
• Primordial gravitational waves from the space-condensate inflation model