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In this paper, we focus on testing gravity theories in the radiative regime using pulsar timing array observations. After reviewing current techniques to measure the dispersion and alternative polarization of gravitational waves, we extend the framework to the most general situations, where the combinations of a massive graviton and alternative polarization modes are considered. The atlas of the Hellings-Downs functions is completed by the new calculations for these dispersive alternative polarization modes. We find that each mode and corresponding graviton mass introduce characteristic features in the Hellings-Downs function. Thus, in principal, we can not only detect each polarization mode, measure the corresponding graviton mass, but also discriminate the different scenarios. In this way, we can test gravity theories in the radiative regime in a generalized fashion, and such method is a direct experiment, where one can address the gauge symmetry of the gravity theories in their linearised limits. Although current pulsar timing still lacks enough stable pulsars and sensitivity for such practices, we expect that future telescopes with larger collecting area could make such experiments be feasible.
General relativity has predicted the existence of gravitational waves (GW), which are waves of the distortions of space-time with two degrees of polarization and the propagation speed of light. Alternative theories predict more polarizations, up to a
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 partic
We introduce a technique for gravitational-wave analysis, where Gaussian process regression is used to emulate the strain spectrum of a stochastic background using population-synthesis simulations. This leads to direct Bayesian inference on astrophys
We have begun an exciting era for gravitational wave detection, as several world-leading experiments are breaching the threshold of anticipated signal strengths. Pulsar timing arrays (PTAs) are pan-Galactic gravitational wave detectors that are alrea
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