Beyond the Hellings–Downs curve: Non-Einsteinian gravitational waves in pulsar timing array correlations

Abstract

Pulsar timing arrays (PTAs) have revealed galaxy-size gravitational waves (GWs) in the form of a stochastic gravitational wave background (SGWB), correlating the radio pulses emitted by millisecond pulsars. This discovery naturally leads to the question of the origin and the nature of the SGWB; the latter is synonymous to testing how quadrupolar the inter-pulsar spatial correlation is. In this paper, we investigate the nature of the SGWB by considering correlations beyond the Hellings-Downs (HD) curve of Einstein's general relativity. We scrutinize the HD and non-Einsteinian GW correlations with the North American Nanohertz Observatory for Gravitational Waves and the Chinese PTA data, and find that both data sets allow a graviton mass of $m_ g eV /c^2$ and subluminal traveling waves. We discuss gravitational physics scenarios beyond general relativity that could host non-Einsteinian GW correlations in the SGWB and highlight the importance of the cosmic variance inherited from stochastic variations across realizations in interpreting PTA observations.