Constraints on primordial curvature power spectrum with pulsar timing arrays

TL;DR

This paper investigates the primordial curvature power spectrum using pulsar timing array data, comparing single- and double-peak models through Bayesian inference, but finds current data insufficient to distinguish between them.

Contribution

It introduces a comprehensive Bayesian analysis of various primordial power spectrum models using pulsar timing data, highlighting the current limitations in model discrimination.

Findings

No significant preference for single- or double-peak models

Current pulsar timing data cannot distinguish different power spectrum shapes

Bayes factors among models are less than 1, indicating weak evidence

Abstract

The stochastic signal detected by NANOGrav, PPTA, EPTA, and CPTA can be explained by the scalar-induced gravitational waves. In order to determine the scalar-induced gravitational waves model that best fits the stochastic signal, we employ both single- and double-peak parameterizations for the power spectrum of the primordial curvature perturbations, where the single-peak scenarios include the $\delta$-function, box, lognormal, and broken power law model, and the double-peak scenario is described by the double lognormal form. Using Bayesian inference, we find that there is no significant evidence for or against the single-peak scenario over the double-peak model, with $\log$ (Bayes factors) among these models $\ln \mathcal{B} < 1$. Therefore, we cannot distinguish the different shapes of the power spectrum of the primordial curvature perturbation with the current sensitivity of pulsar timing arrays.