Pulsar-timing arrays, astrometry, and gravitational waves

TL;DR

This paper develops a comprehensive theoretical framework using the TAM formalism to analyze pulsar-timing and astrometry data for detecting and characterizing a stochastic gravitational-wave background, including non-Einsteinian polarizations.

Contribution

It introduces the TAM approach for cosmological perturbations to compute power spectra and correlation functions for gravitational waves, extending analysis to alternative gravity theories.

Findings

Derived angular power spectra for standard and non-Einsteinian polarizations.

Showed how pulsar-timing and astrometry can be combined for cross-validation.

Highlighted the importance of testing gravitational-wave polarization chirality.

Abstract

We discuss the theory of pulsar-timing and astrometry probes of a stochastic gravitational-wave background with a recently developed "total-angular-momentum" (TAM) formalism for cosmological perturbations. We review the formalism, emphasizing in particular the features relevant for this work and describe the observables we consider (i.e. the pulsar redshift and stellar angular displacement). Using the TAM approach, we calculate the angular power spectra for the observables and from them derive angular auto- and cross-correlation functions. We provide the full set of power spectra and correlation functions not only for the standard transverse-traceless propagating degrees of freedom in general relativity, but also for the four additional non-Einsteinian polarizations that may arise in alternative-gravity theories. We discuss how pulsar-timing and astrometry surveys can complement and serve as cross checks to one another and comment on the importance of testing the chirality of the gravitational-wave background as a tool to understand the nature of its sources. A simple rederivation of the power spectra from the plane-wave formalism is provided in an Appendix.