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

¹ Asia Pacific Center for Theoretical Physics, Pohang 37673, Republic of Korea
² Institute of Physics, Academia Sinica, Taipei 11529, Taiwan
³ Institute of Astronomy and Astrophysics, Academia Sinica, Taipei 11529, Taiwan

^★ Corresponding authors; reginald.bernardo@apctp.org, nkw@phys.sinica.edu.tw

Received: 4 February 2024
Accepted: 28 September 2024

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 ≲ 1.04 × 10⁻²² eV/c² 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.