Constraints on ultra-slow-roll inflation with the NANOGrav 15-Year dataset

Abstract

Ultra-slow-roll (USR) inflation predicts an exponential amplification of scalar perturbations at small scales, which leads to a stochastic gravitational wave background (SGWB) through the coupling of the scalar and tensor modes at the second-order expansion of the Einstein equation. In this work, we search for such a scalar-induced SGWB from the NANOGrav 15-year (NG15) dataset, and find that the SGWB from USR inflation could explain the observed data. The Bayes factors are 54 ± 5 for the USR inflation model alone and 68 ± 6 for the combined USR inflation plus supermassive black hole binaries (SMBHB) models. We place constraints on the amplitude of the scalar power spectrum to PRp > 10-1.95 at 95% confidence level (C.L.) at the scale of k ∼ 20 pc-1. We find that log10PRp degenerates with the peak scale log10kp. We also obtain the parameter space allowed by the data in the USR inflationary scenario, where the e-folding numbers of the duration of the USR phase has a lower limit ΔN > 2.80 (95% C.L.) when the USR phase ends at N ≈ 20. With astrophysically motivated priors, the NG15 dataset fits both the USR inflation model and SMBHB model equally well.