Lorentz violation with gravitational waves: Constraints from NANOGrav and IPTA data

We explore a theoretical framework in which Lorentz symmetry is explicitly broken by incorporating derivative terms of the extrinsic curvature into the gravitational action. These modifications introduce a scale-dependent damping effect in the propagation of gravitational waves (GWs), governed by a characteristic energy scale denoted as $M_{\text{LV}}$. Tightest constraints on $M_{\text{LV}}$ are achieved when we assume GWs have a primordial origin. In this scenario, we derive the modified spectral energy density of GWs and confront it with recent observational data from the NANOGrav 15-year dataset and the second data release of the International Pulsar Timing Array (IPTA). Our analysis yields a lower bound on the Lorentz-violating energy scale, finding $M_{\text{LV}}>{10}^{-19}$ GeV at 68% confidence level. This result significantly improves upon previous constraints derived from LIGO/VIRGO binary merger observations. Our findings demonstrate the potential of pulsar timing arrays to probe fundamental symmetries of spacetime and offer new insights into possible extensions of general relativity.