Charting the Nanohertz Gravitational Wave Sky with Pulsar Timing Arrays

TL;DR

This paper reviews the theoretical foundations and current understanding of the nanohertz gravitational wave background detected by pulsar timing arrays, discussing key questions, constraints, and future research directions.

Contribution

It provides a comprehensive theoretical derivation of the expected gravitational wave signal and explores future milestones and emerging considerations in PTA science.

Findings

Detection of a nanohertz stochastic gravitational wave background

Current constraints on the gravitational wave signal

Discussion of future theoretical and observational milestones

Abstract

In the summer of 2023, the pulsar timing arrays (PTAs) announced a compelling evidence for the existence of a nanohertz stochastic gravitational wave background (SGWB). Despite this breakthrough, however, several critical questions remain unanswered: What is the source of the signal? How can cosmic variance be accounted for? To what extent can we constrain nanohertz gravity? When will individual supermassive black hole binaries become observable? And how can we achieve a stronger detection? These open questions have spurred significant interests in PTA science, making this an opportune moment to revisit the astronomical and theoretical foundations of the field, as well as the data analysis techniques employed. In this review, we focus on the theoretical aspects of the SGWB as detected by PTAs. We provide a comprehensive derivation of the expected signal and its correlation, presented in a pedagogical manner, while also addressing current constraints. Looking ahead, we explore future milestones in the field, with detailed discussions on emerging theoretical considerations such as cosmic variance, the cumulants of the one- and two-point functions, subluminal gravitational waves, and the anisotropy and polarization of the SGWB.