Pulsar and cosmic variances of pulsar timing-array correlation measurements of the stochastic gravitational wave background

TL;DR

This paper develops a general, efficient method to calculate the expected correlation and its variance in pulsar timing-array measurements of the stochastic gravitational wave background, accounting for various uncertainties.

Contribution

It introduces a comprehensive, numerically efficient framework for computing pulsar and cosmic variances in gravitational wave background correlation measurements, including non-Einstein modes and off-light-cone effects.

Findings

Derived mean and variance formulas for Hellings-Downs correlation

Incorporated arbitrary pulsar distances and gravitational wave modes

Provided a general method applicable to various gravitational theories

Abstract

Pulsar timing-array correlation measurements offer an exciting opportunity to test the nature of gravity in the cosmologically novel nanohertz gravitational wave regime. The stochastic gravitational wave background is assumed Gaussian and random, while there are limited pulsar pairs in the sky. This brings theoretical uncertainties to the correlation measurements, namely the pulsar variance due to pulsar samplings and the cosmic variance due to Gaussian signals. We demonstrate a straightforward calculation of the mean and the variances on the Hellings-Downs correlation relying on a power spectrum formalism. We keep arbitrary pulsar distances and consider gravitational wave modes beyond Einstein gravity as well as off the light cone throughout, thereby presenting the most general and, most importantly, numerically efficient calculation of the variances.