Probing the shape of the primordial curvature power spectrum and the energy scale of reheating with pulsar timing arrays

TL;DR

This paper investigates how pulsar timing array data can reveal details about the primordial curvature spectrum and reheating energy scale, using Bayesian analysis to interpret recent gravitational wave observations.

Contribution

It models the primordial curvature power spectrum with a lognormal form and constrains the reheating temperature using NANOGrav data, providing new insights into early Universe physics.

Findings

Narrow peak in primordial power spectrum ($\

Reheating temperature lower bound $T_{rh} \\geq 0.1$ GeV.

Detection of a turning point in the SIGW spectrum around $f \\sim 10^{-8.1}$ Hz.

Abstract

The stochastic gravitational wave background (SGWB) provides a unique opportunity to probe the early Universe, potentially encoding information about the primordial curvature power spectrum and the energy scale of reheating. Recent observations by collaborations such as NANOGrav, PPTA, EPTA+InPTA, and CPTA have detected a stochastic common-spectrum signal, which may originate from scalar-induced gravitational waves (SIGWs) generated by primordial curvature perturbations during inflation. In this study, we explore the hypothesis that the NANOGrav signal is sourced by SIGWs and aim to constrain the shape of the primordial curvature power spectrum and the reheating energy scale using the NANOGrav 15-year data set. We model the primordial curvature power spectrum with a lognormal form and focus on the case where the equation of state during reheating is $w=1/6$, corresponding to an inflaton potential $V(\phi) \sim \phi^{14/5}$. Employing Bayesian inference, we obtain posterior distributions for the lognormal power spectrum parameters and the reheating temperature. Our results indicate a narrow peak in the primordial power spectrum ($\Delta < 0.001$ at 90\% confidence) and a lower bound on the reheating temperature ($T_{\rm rh} \geq 0.1 {\rm GeV}$), consistent with Big Bang Nucleosynthesis constraints. The best-fit SIGW energy density spectrum exhibits a distinct turning point around $f \sim 10^{-8.1}\,{\rm Hz}$, corresponding to the transition from reheating to the radiation-dominated era. This feature, combined with the sharp high-frequency decrease due to the narrow primordial power spectrum peak, offers a unique signature for probing early Universe properties.