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

TL;DR

This paper introduces a model-independent method to reconstruct the primordial curvature power spectrum from PTA data, simplifying the assessment of whether SIGWs can explain observed gravitational-wave signals.

Contribution

It presents a novel, free-spectrum reconstruction approach that bypasses complex energy density calculations for evaluating SIGWs against PTA observations.

Findings

Reconstructed the primordial curvature power spectrum over a broad range of scales.

Demonstrated that the method simplifies testing SIGW models against PTA data.

Provided a framework for model-independent analysis of gravitational-wave origins.

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 $10^{1}\,\mathrm{Mpc}^{-1}$ to $10^{20}\,\mathrm{Mpc}^{-1}$ with NANOGrav 15-yrs 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.