Pulsar and cosmic variances of pulsar timing-array correlation measurements of the stochastic gravitational wave background

Abstract

Pulsar timing-array correlation measurements offer an exciting opportunity to test the nature of gravity in the cosmologically novel nanohertz gravitational wave regime. The stochastic gravitational wave background is assumed Gaussian and random, while there are limited pulsar pairs in the sky. This brings theoretical uncertainties to the correlation measurements, namely the pulsar variance due to pulsar samplings and the cosmic variance due to Gaussian signals. We demonstrate a straightforward calculation of the mean and the variances on the Hellings-Downs correlation relying on a power spectrum formalism. We keep arbitrary pulsar distances and consider gravitational wave modes beyond Einstein gravity as well as off the light cone throughout, thereby presenting the most general and, most importantly, numerically efficient calculation of the variances.

25 pages, 6 figures, minor changes, to appear in JCAP, code in https://github.com/reggiebernardo/PTAfast

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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
• Dissecting the Stochastic Gravitational Wave Background with Astrometry
• Testing gravity with cosmic variance-limited pulsar timing array correlations
• Status Report on Global Pulsar-Timing-Array Efforts to Detect Gravitational Waves
• 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
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• The impact of large-scale galaxy clustering on the variance of the Hellings-Downs correlation: theoretical framework
• 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
• Posterior predictive checking for gravitational-wave detection with pulsar timing arrays: II. Posterior predictive distributions and pseudo Bayes factors
• Measuring anisotropies in the PTA band with cross-correlations
• Mitigating cosmic variance in the Hellings-Downs curve: a Cosmic Microwave Background analogy
• Pulsar timing and polarimetry: results and perspectives
• The impact of large-scale galaxy clustering on the variance of the Hellings-Downs correlation: numerical results
• Connecting Inflation to the NANOGrav 15-year Data Set via Massive Gravity
• Search for the non-linearities of gravitational wave background in NANOGrav 15-year data set
• Accurate pulsar timing array residual variances and correlation of the stochastic gravitational wave background
• Estimating the gravitational wave background anisotropy: a Bayesian approach boosted by cross-correlation angular power spectrum
• Identifying the Quadrupolar Nature of Gravitational Wave Background through Space-based Missions
• Spatial Correlation between Pulsars from Interfering Gravitational-Wave Sources in Massive Gravity