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

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.