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 $M_{{LV}}$ . We derive the modified spectral energy density of GWs within this model 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 $M_{{LV}} > 10^{-19}$ 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.