Testing Gravity with Realistic Gravitational Waveforms in Pulsar Timing Arrays

TL;DR

This paper explores how relaxing the assumption of uncorrelated frequencies in gravitational wave backgrounds affects pulsar timing array analyses, enabling potential insights into fundamental physics and wave dispersion.

Contribution

It develops a formalism to incorporate correlated frequency effects in PTA data analysis, including realistic waveforms like binary inspirals, and assesses the validity of the monochromatic approximation.

Findings

Correlated frequency effects can reveal information about wave dispersion.

The monochromatic approximation remains valid for slowly evolving frequencies.

Scaling relations quantify the approximation's accuracy.

Abstract

We consider the effects of relaxing the assumption that gravitational waves composing the stochastic gravitational wave background (SGWB) are uncorrelated between frequencies in analyses of the data from Pulsar Timing Arrays (PTAs). While individual monochromatic plane waves are often a good approximation, a background composed of unresolved astrophysical sources cannot be exactly uncorrelated since an infinite plane wave propagates no temporal signal. We consider how relaxing this assumption allows us to extract potential information about modified dispersion relations and other fundamental physics questions, as both the group and phase velocity of waves become relevant. After developing the formalism we carry out simple Gaussian wavepacket examples and then consider more realistic waveforms, such as that from binary inspirals. When the frequency evolves only slowly across the PTA temporal baseline, the monochromatic assumption at an effective mean frequency remains a good approximation and we provide scaling relations that characterize its accuracy.