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General relativity predicts that gravitational waves propagate at the speedof light. Although ground-based gravitational-wave detectors have successfullyconstrained the velocity of gravitational waves in the high-frequency range,extending this constraint to the lower frequency range remains a challenge. Inthis work, we utilize the deviations in the overlap reduction function for agravitational-wave background within pulsar timing arrays to investigate thevelocity of gravitational waves in the nanohertz frequency band. By analyzingthe NANOGrav 15-year data set, we obtain a well-constrained lower bound for thevelocity of gravitational waves that $v \gtrsim 0.87\,c$, where $c$ is thespeed of light.

Constraints on the velocity of gravitational waves from NANOGrav 15-year data set