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

TL;DR

The paper investigates how realistic interference among nanohertz gravitational-wave sources, within the framework of massive gravity, alters the spatial correlation patterns in pulsar timing arrays. It derives the redshift cross-correlation and the overlap reduction function, showing that interference introduces a strong dependence on source phases and sky locations, while parity constraints negate certain cross-terms. Through extensive simulations, the authors demonstrate that the resulting correlations are well described by a Legendre expansion dominated by the quadrupole, with the l=2 coefficient increasing as the graviton mass grows (via a lower $\eta$), yet the off-diagonal interference induces large cosmic variance that obscures discrimination between massive gravity and GR from a single Universe. They conclude that, beyond the fundamental observation-time bound, achieving substantially tighter graviton-mass limits with PTAs is statistically challenging under realistic conditions, though the spectral floor set by $f_{\min}=m_g/(2\pi)$ remains a primary constraint. For cosmological stochastic backgrounds, ensemble averaging would reduce interference-induced variance and could preserve discriminatory power between gravity theories. $\,$

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.