Correlations for an anisotropic polarized stochastic gravitational wave background in pulsar timing arrays

TL;DR

This paper derives a comprehensive formula for the correlation signatures of an anisotropic, polarized stochastic gravitational wave background in pulsar timing arrays, enabling tests of gravity and polarization modes beyond Einstein's theory.

Contribution

It extends the harmonic space analysis to include anisotropy and polarization, providing new tools for testing gravitational theories with pulsar timing data.

Findings

Derived a general correlation formula for anisotropic polarized backgrounds.

Identified signatures dependent on gravitational wave speed and pulsar distances.

Proposed tests for isotropy and non-Einsteinian polarizations in nanohertz gravitational waves.

Abstract

The recent compelling observation of the nanohertz stochastic gravitational wave background has brought to light a new galactic arena to test gravity. In this paper, we derive a formula for the most general expression of the stochastic gravitational wave background correlation that could be tested with pulsar timing and future square kilometer arrays. Our expressions extends the harmonic space analysis, also often referred to as the power spectrum approach, to predict the correlation signatures of an anisotropic polarized stochastic gravitational wave background with subluminal tensor, vector, and scalar gravitational degrees of freedom. We present the first few nontrivial anisotropy and polarization signatures in the correlation and discuss their dependence on the gravitational wave speed and pulsar distances. Our results set up tests that could potentially be used to rigorously examine the isotropy of the stochastic gravitational wave background and strengthen the existing constraints on possible non-Einsteinian polarizations in the nanohertz gravitational wave regime.