Testing Gravity with Frequency-Dependent Overlap Reduction Function in Pulsar Timing Array

TL;DR

This paper explores how the frequency-dependent overlap reduction function in pulsar timing arrays can be used to test modified gravity theories by constraining the phase velocity of gravitational waves in the nano-hertz band.

Contribution

It provides analytical expressions for the multipole moments of the ORF and applies them to constrain phase velocity using Chinese PTA data, highlighting potential for testing gravity theories.

Findings

Constraints on subluminal phase velocity from PTA data.

Analytical expressions for multipole moments of the ORF.

Potential to explore modified gravity in nano-hertz gravitational wave background.

Abstract

The positive evidence of a nano-hertz gravitational wave background recently found by several pulsar timing array (PTA) collaborations opened up a window to test modified gravity theories in a unique frequency band in parallel to other gravitational wave detection experiments. In particular, the overlap reduction function (ORF) in PTA observation is sensitive to the phase velocity of gravitational waves. In this work, we provide analytical expressions for the coefficients of the multipole moments in the ORF, and utilize these analytical results to study constraints on the phase velocity from the frequency dependent overlap reduction function obtained from the Chinese PTA (CPTA) data. While the data contain large error bars yet, interesting constraints are found in the frequency-dependent ORF in the case of subluminal phase velocity. This makes us expect that the nano-hertz band gravitational wave background will become one of the important arenas for exploring modified gravity theories.