Stochastic gravitational wave background phenomenology in a pulsar timing array

Constraining gravitational wave propagation using pulsar timing array correlations

“…The overlap reduction function (ORF), Γ ab (ζ), or the PTA's spatial correlation observable, is obtained simply by normalizing γ ab (ζ) such that Γ ab (0) = 0.5 for tensors with v = 1. We refer the reader to [31,32] for a detailed description of this procedure, and a derivation of the results put forward in this section.…”

“…The autocorrelation, γ aa , embodying a pulsar's correlation with itself, is also of relevance in this work. This physical quantity admits analytical expressions, as one dimensional integrals, which we give below for the tensor and vector modes [31]: for tensor polarizations the autocorrelation is…”

“…(9) For our purposes, we apply PTAfast [33] which implements all the intervening calculations, and provides the ORF's and autocorrelations relevant for comparison with observations.…”

“…We implement these steps using PTAfast [33] together with the cosmology community code Cobaya [39], and analyze the results using GetDist [40]. Our codes and resulting MCMC chains are publicly accessible in GitHub.…”

“…Adding to the science prospects of PTAs, in this work, we take a conservative stand on SGWB correlations and consider subluminal GW modes as a source of the observed cross correlations in a PTA [30][31][32]. We use the public code PTAfast [33] and the correlations data set by NANOGrav to constrain the GW speed, and henceforth give its take on the graviton mass.…”