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

The recent astronomical milestone by the pulsar timing arrays (PTA) has revealed galactic-size gravitational waves (GW) in the form of a stochastic gravitational wave background (SGWB), correlating the radio pulses emitted by millisecond pulsars. This draws the outstanding questions toward 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 tackle the nature of the SGWB by considering correlations beyond the Hellings-Downs (HD) curve of Einstein's general relativity. We put the HD and non-Einsteinian GW correlations under scrutiny with the NANOGrav and the CPTA data, and find that both data sets allow a graviton mass $m_{\rm g} \lesssim 1.04 \times 10^{-22} \ {\rm eV}/c^2$ 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 the stochasticity in interpreting PTA observation.