Spatial Correlation between Pulsars from Interfering Gravitational-Wave Sources in Massive Gravity

TL;DR

This paper explores how interference of gravitational waves from multiple sources affects pulsar timing array correlations in massive gravity, revealing increased variability and challenges in constraining graviton mass.

Contribution

It introduces a simulation-based analysis of interference effects on PTA correlations within massive gravity, highlighting the impact on graviton mass bounds.

Findings

Correlation patterns remain quadrupolar but vary with interference.

Interference causes significant variability, complicating gravity tests.

Tighter graviton mass constraints are statistically and observationally challenging.

Abstract

In the nanohertz band, the spatial correlations in pulsar timing arrays (PTAs) produced by interfering gravitational waves (GWs) from multiple sources likely deviate from the traditional ones without interference under the assumption of an isotropic Gaussian ensemble. This work investigates the impact of such interference within the framework of massive gravity. Through simulations, we show that while the resulting correlation patterns can be described by Legendre expansions with coefficients that depend on the interference configuration, they remain predominantly quadrupolar (l = 2), with this feature becoming more pronounced as the graviton mass increases--reflecting both the tensorial polarizations and the modified GW dispersion. However, the interference introduces significant variability in the angular correlation, making it difficult to distinguish massive gravity from general relativity based on a single realization of the Universe. We conclude that beyond a fundamental constraint set by the PTA observation time, achieving a substantially tighter bound on the graviton mass is statistically challenging and observationally limited under realistic conditions.