Relic gravitational waves in the frame of slow-roll inflation with a power-law potential and the detection

TL;DR

This paper derives analytic solutions for relic gravitational waves in slow-roll inflation with a power-law potential, analyzing their spectrum and prospects for detection by future GW observatories.

Contribution

It provides new analytic solutions for RGWs in slow-roll inflation with a power-law potential and explores parameter constraints and detection prospects.

Findings

High-frequency RGW spectrum depends on inflation and reheating parameters.

Future GW detectors like SKA, eLISA, BBO, DECIGO can detect RGWs.

BBO and DECIGO can test quantum normalization and parameter distinctions.

Abstract

We obtained the analytic solutions of relic gravitational waves (RGWs) for the slow-roll inflation with a power-law form potential of the scalar field, $V=\lambda\phi^n$. Based on a reasonable range of $n$ constrained by cosmic microwave background (CMB) observations, we give tight constraints of the tensor-to-scalar ratio $r$ and the inflation expansion index $\beta$ for the fixed scalar spectral index $n_s$. Even though, the spectrum of RGWs in low frequencies is hardly depends on any parameters, the high frequency parts will be affected by several parameters, such as $n_s$, the reheating temperature $T_{RH}$ and the index $\beta_s$ describing the expansion from the end of inflation to the reheating process. We analyzed in detail all the factors which would affect the spectrum of RGWs in high frequencies including the quantum normalization. We found that the future GW detectors SKA, eLISA, BBO and DECIGO are promising to catch the signals of RGWs. Furthermore, BBO and DECIGO have the potential not only to distinguish the spectra with different parameters but also to examine the validity of the quantum normalization.