The impact of large-scale galaxy clustering on the variance of the Hellings-Downs correlation

The origin of the stochastic gravitational wave (GW) background, recently discovered from pulsar timing array experiments, is still unclear. If this background is of astrophysical origin, we expect the distribution of GW sources to follow the one of galaxies. Since galaxies are not perfectly isotropically distributed at large scales, but follow the cosmological large-scale structure, this would lead to an intrinsic anisotropy in the distribution of GW sources. In this work, we develop a formalism to account for this anisotropy, by considering a Gaussian ensemble of sources in each realization of the universe and then taking ensemble averages over all such realizations. We find that large-scale galaxy clustering has no impact on the Hellings-Downs curve, describing the expectation value of pulsar timing residual correlations. However, it introduces a new contribution to the variance of the Hellings-Downs correlation. Hence, due to the anisotropic distribution of sources, the measurements of pulsar timing residual correlations in our Universe may differ from the Hellings-Downs curve. This indicates that the variance of the Hellings-Downs correlation can be utilized as a new cosmological observable that might help us to unveil the nature of current background observations in the nHz band.