Revisit relic gravitational waves based on the latest CMB observations

TL;DR

This paper recalculates relic gravitational wave spectra using latest CMB data, linking inflation parameters to observational constraints, and assesses their detectability with current and future gravitational wave detectors.

Contribution

It provides updated relations between inflation parameters and relic gravitational wave spectra based on recent CMB observations, and evaluates their detectability.

Findings

Recalculated reheating temperature with WMAP 7 data.

Established relation between tensor-to-scalar ratio and inflation index.

Discussed detectability of relic gravitational waves with current and planned detectors.

Abstract

According to the CMB observations, Mielczarek (\cite{Mielczarek}) evaluated the reheating temperature, which could help to determine the history of the Universe. In this paper, we recalculate the reheating temperature using the new data from WMAP 7 observations. Based on that, we list the approximate solutions of relic gravitational waves (RGWs) for various frequency bands. With the combination of the quantum normalization of RGWs when they are produced and the CMB observations, we obtain the relation between the tensor-to-scalar ratio $r$ and the inflation index $\beta$ for a given scalar spectral index $n_s$. As a comparison, the diagram $r-\beta$ in the slow-roll inflation model is also given. Thus, the observational limits of $r$ from CMB lead to the constraints on the value of $\beta$. Then, we illustrate the energy density spectrum of RGWs with the quantum normalization for different values of $r$ and the corresponding $\beta$. For comparison, the energy density spectra of RGWs with parameters based on slow-roll inflation are also discussed. We find that the values of $n_s$ affect the spectra of RGWs sensitively in the very high frequencies. Based on the current and planed gravitational wave detectors, we discuss the detectabilities of RGWs.