Pulse redshift of pulsar timing array signals for all possible gravitational wave polarizations in modified general relativity

Abstract

Pulsar timing arrays (PTA) have the promise to detect gravitational waves (GWs) from sources which are in a unique frequency range of 10^-9 - 10^-6 Hz. This in turn also provides an opportunity to test the theory of general relativity in the low frequency regime. The central concept of the detection of GWs with PTA lies in measuring the time of arrival difference of the pulsar signal due to the passing of GWs i.e. the pulses get red-shifted. In this paper we provide a complete derivation of the redshift computation for all six possible polarizations of GW which arise due to the modifcations to general relativity. We discuss the smoothness of the redshift and related properties at the critical point, where the GW source lies directly behind the pulsar. From our mathematical discussion we conclude that the redshift has to be split differently into polarization part (pattern functions) and interference part, to avoid discontinuities and singularities in the pattern functions. This choice of pattern functions agrees with the formula one uses for interferometers with a single detector arm. Finally, we provide a general expression which can in principle be used for pulsars and GW of any frequency without invoking the low frequency assumption and using said assumption we develop the expression up to first order in the strain and find correction terms to the canonical redshift formula.

arXiv commentAccepted for publication in PRD

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• Principles of Gravitational-Wave Detection with Pulsar Timing Arrays
• Fundamental Physics and Cosmology with TianQin
• Analytic series expansion of the overlap reduction function for gravitational wave search with pulsar timing arrays
• Non-linear corrections of overlap reduction functions for pulsar timing arrays
• Unveiling the existence of nontensorial gravitational-wave polarizations from individual supermassive black hole binaries with pulsar timing arrays
• Overlap reduction function for gravitational wave detectors in an expanding Universe
• Series expansion of the overlap reduction function for scalar and vector polarizations for gravitational wave search with pulsar timing arrays
• Testing No slip model with pulsar timing arrays: NANOGrav and IPTA