Mapping gravitational-wave backgrounds in modified theories of gravity using pulsar timing arrays

TL;DR

This paper develops methods to map and analyze gravitational-wave backgrounds with non-GR polarizations using pulsar timing arrays, providing analytic response functions and exploring sensitivities to various polarization modes.

Contribution

It extends previous CMB-based mapping techniques to non-GR gravitational-wave polarizations and derives analytic response and overlap reduction functions for pulsar timing arrays.

Findings

Analytic pulsar-timing response functions for non-GR polarizations.

Overlap reduction functions for scalar-transverse and vector-longitudinal modes.

Pulsar timing is insensitive to certain polarization anisotropies beyond specific multipole orders.

Abstract

We extend our previous work on applying CMB techniques to the mapping of gravitational-wave backgrounds to backgrounds which have non-GR polarisations. Our analysis and results are presented in the context of pulsar-timing array observations, but the overarching methods are general, and can be easily applied to LIGO or eLISA observations using appropriately modified response functions. Analytic expressions for the pulsar-timing response to gravitational waves with non-GR polarisation are given for each mode of a spin-weighted spherical-harmonic decomposition of the background, which permit the signal to be mapped across the sky to any desired resolution. We also derive the pulsar-timing overlap reduction functions for the various non-GR polarisations, finding analytic forms for anisotropic backgrounds with scalar-transverse ("breathing") and vector-longitudinal polarisations, and a semi-analytic form for scalar-longitudinal backgrounds. Our results indicate that pulsar-timing observations will be completely insensitive to scalar-transverse mode anisotropies in the polarisation amplitude beyond dipole, and anisotropies in the power beyond quadrupole. Analogously to our previous findings that pulsar-timing observations lack sensitivity to tensor-curl modes for a transverse-traceless tensor background, we also find insensitivity to vector-curl modes for a vector-longitudinal background.