Model-independent reconstruction of the primordial curvature power spectrum from PTA data

Abstract

Abstract Recently released data from pulsar timing array (PTA) collaborations provide strong evidence for a stochastic signal consistent with a gravitational-wave background, potentially originating from scalar-induced gravitational waves (SIGWs). However, in order to determine whether the SIGWs with a specific power spectrum of curvature perturbations can account for the PTA signal, one needs to estimate the energy density of the SIGWs, which can be computationally expensive. In this paper, we use a model-independent approach to reconstruct the primordial curvature power spectrum using a free spectrum cross over from 101 Mpc-1 to 1020 Mpc-1 with NANOGrav 15-year data set. Our results can simplify the task of assessing whether a given primordial curvature power spectrum can adequately explain the observed PTA signal without calculating the energy density of SIGWs.