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The recent compelling observation of the nanohertz stochastic gravitationalwave background has brought to light a new galactic arena to test gravity. Inthis paper, we derive a formula for the most general expression of thestochastic gravitational wave background correlation that could be tested withpulsar timing and future square kilometer arrays. Our expressions extends theharmonic space analysis, also often referred to as the power spectrum approach,to predict the correlation signatures of an anisotropic polarized stochasticgravitational wave background with subluminal tensor, vector, and scalargravitational degrees of freedom. We present the first few nontrivialanisotropy and polarization signatures in the correlation and discuss theirdependence on the gravitational wave speed and pulsar distances. Our resultsset up tests that could potentially be used to rigorously examine the isotropyof the stochastic gravitational wave background and strengthen the existingconstraints on possible non-Einsteinian polarizations in the nanohertzgravitational wave regime.

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