Forecasting Sensitivity to Modified Dispersion Effects in Pulsar Timing Arrays

TL;DR

This paper forecasts how pulsar timing arrays can detect deviations in gravitational wave dispersion relations, focusing on phase velocity uncertainties and the timeline for observing specific deviations.

Contribution

It provides a comprehensive Fisher analysis to predict PTA sensitivity to modified dispersion relations, including sample variance and non-Gaussian effects.

Findings

Detecting 10% deviation in phase velocity requires about 30 years of data.

Detection of -1% deviation at 3σ level also requires approximately 30 years.

The analysis accounts for non-Gaussian behavior and sample variance effects.

Abstract

The pulsar timing array systems have reported a detection of a nanohertz-band stochastic gravitational wave background in our galaxy. It is of interest to use this observation to probe modified gravity and to forecast the sensitivity with which certain deviations can be tested in the coming years. In this paper, we focus on the modified dispersion relation of the tensor modes and its effect on the overlap reduction function of the timing residual cross-correlations. We perform a comprehensive forecast of the phase velocity uncertainty, $\sigma_v$, using a Fisher analysis validated by a mock-data study to account for potential non-Gaussian behavior. We also take into account the sample variance effect and provide an observational timeline for future PTA sensitivity: detecting a $10\%$ or $-1\%$ deviation from the speed of light at the $3\sigma$ level requires $\mathcal{O}(30)$ years of observations.