Finite-distance effects and scalar suppression in massive gravity

Abstract

Pulsar timing arrays (PTAs) probe the stochastic gravitational wave (GW) background through the angular cross-correlations of timing residuals. For a GW background in general relativity (GR), the expected overlap reduction function (ORF) is given by the Hellings--Downs (HD) correlation. We investigate how a nonzero graviton mass modifies this prediction through a massive dispersion relation and additional vector and scalar polarizations, producing a modified effective ORF. In the massive limit, the finite-distance pulsar terms survive angular averaging, multiplying the correlations of all three polarization sectors by a pulsar-dependent factor that can enhance, suppress, or reverse them. We adopt a tensor Earth--Earth normalization that preserves the continuous finite-distance effect. In the massless limit, we find that the vector ORF vanishes and the scalar ORF approaches a finite breathing mode. We propose the phenomenological prescription $Ω_S/Ω_T=A_S(m_g/ω)^{n_S}$, with scalar amplitude parameter $A_S$ and suppression index $n_S>0$. These results provide a consistent framework for future PTA analyses of massive gravity.