Forecasting graviton-mass constraints from the full covariance of PTA-astrometry ORF estimators

TL;DR

This paper develops a full-covariance formalism for PTA-astrometry estimators to forecast constraints on graviton mass from a stochastic gravitational-wave background, showing significant improvements with future observatories.

Contribution

It introduces a comprehensive covariance framework for PTA-astrometry overlap reduction function estimators and applies it to forecast graviton-mass bounds.

Findings

Current bounds: $m_g<4.41\times10^{-24}$ eV/c^2 with NANOGrav and Gaia.

Future bounds: $m_g<0.48\times10^{-24}$ eV/c^2 with SKA and Theia/Gaia-NIR.

Astrometric channels significantly enhance graviton-mass constraints in future configurations.

Abstract

We develop a full-covariance formalism for pulsar timing array(PTA) -- astrometry verlap reduction function (ORF) estimators and use it to forecast graviton-mass constraints from a nanohertz stochastic gravitational-wave background (SGWB). Analytic covariance expressions are derived for auto- and cross-channel ORF estimators, including signal-signal, noise-noise, and signal-noise contributions, and are validated against numerical simulations. For an observational configuration with sensitivities comparable to NANOGrav and Gaia, we obtain an expected joint 90\% upper limit of $m_g<4.41\times10^{-24}\,\mathrm{eV}/c^2$, which remains PTA-dominated and lies at the same order of magnitude as the existing NANOGrav 15-year PTA-only bound. For a future-like configuration with sensitivities comparable to the SKA and Theia/Gaia-NIR, the astrometric channels contribute significantly to the constraining power, and the joint limit improves to $m_g<0.48 \times 10^{-24} \, \mathrm{eV}/c^2$. These forecasts indicate that PTA -- astrometry multichannel inference provides a viable avenue for improving graviton-mass constraints under next-generation observational conditions.