Stochastic gravitational wave background phenomenology in a pulsar timing array

Abstract

Pulsar timing offers an independent avenue to test general relativity and alternative gravity theories. This requires an understanding of how metric polarizations beyond the familiar transverse tensor ones imprint as a stochastic gravitational wave background and correlate the arrival time of radio pulses from a pair of millisecond pulsars. In this work, we focus on an isotropic stochastic gravitational wave background and present a straightforward, self-contained formalism for obtaining the power spectrum and the overlap reduction function, the relevant physical observable in a pulsar timing array, for generic gravitational degrees of freedom featuring both transverse and longitudinal modes off the light cone. We additionally highlight our consideration of finite pulsar distances, which we find significant in two ways: first, making all the modes well defined, and second, keeping the small scale power that is contained by pulsars of subdegree separations in the sky. We discuss this for tensor, vector, and scalar polarizations, for each one focusing on the angular power spectrum and the overlap reduction function for an isotropic stochastic gravitational wave background. Our results pave the road for an efficient numerical method for examining the gravitational wave induced spatial correlations across millisecond pulsars in a pulsar timing array.

28 pages, 5 figures, discussion improved, to appear in PRD, see implementation `PTAfast' https://github.com/reggiebernardo/PTAfast

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• Constraining gravitational wave propagation using pulsar timing array correlations
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• A Test of Gravity with Pulsar Timing Arrays
• Search for Non-Tensorial Gravitational-Wave Backgrounds in the NANOGrav 15-Year Data Set
• Testing gravity with cosmic variance-limited pulsar timing array correlations
• Constraints on the velocity of gravitational waves from NANOGrav 15-year data set
• Beyond the Hellings-Downs curve: Non-Einsteinian gravitational waves in pulsar timing array correlations
• Pulsar Timing Array Harmonic Analysis and Source Angular Correlations
• Charting the Nanohertz Gravitational Wave Sky with Pulsar Timing Arrays
• Correlations for an anisotropic polarized stochastic gravitational wave background in pulsar timing arrays
• Measuring kinematic anisotropies with pulsar timing arrays
• Unveiling the Graviton Mass Bounds through Analysis of 2023 Pulsar Timing Array Data Releases
• Harmonic analysis for pulsar timing arrays
• Cosmic variance of the Hellings and Downs correlation for ensembles of universes having nonzero angular power spectra
• Toward a test of Gaussianity of a gravitational wave background
• Angular correlation and deformed Hellings-Downs curve from spin-2 ultralight dark matter
• Measuring anisotropies in the PTA band with cross-correlations
• Mitigating cosmic variance in the Hellings-Downs curve: a Cosmic Microwave Background analogy
• Unveiling the existence of nontensorial gravitational-wave polarizations from individual supermassive black hole binaries with pulsar timing arrays
• Connecting Inflation to the NANOGrav 15-year Data Set via Massive Gravity
• Accurate pulsar timing array residual variances and correlation of the stochastic gravitational wave background
• Graph-based Summary Statistics for Revealing the Stochastic Gravitational Wave Background in Pulsar Timing Arrays
• Full analytic expressions of overlap reduction functions for anisotropies of the stochastic gravitational-wave background with pulsar timing arrays
• Spatial Correlation between Pulsars from Interfering Gravitational-Wave Sources in Massive Gravity