Probing General Relativity on Cosmological Scales in the 2040s

TL;DR

This paper discusses the potential of future large-scale structure surveys in the 2040s to test general relativity on cosmological scales by detecting relativistic effects in galaxy clustering, which are currently unexplored.

Contribution

It proposes a framework for using next-generation surveys to measure relativistic effects in large-scale structure, enabling tests of gravity beyond current capabilities.

Findings

Relativistic effects imprint detectable signatures on galaxy clustering.

Next-generation surveys can measure these effects with high precision.

Detecting these effects would provide new tests of general relativity.

Abstract

General relativity is exquisitely tested in strong-field regimes, yet its validity on cosmological scales remains largely unexplored. Upcoming wide and deep large-scale structure surveys will access the ultra-large, linear scales where relativistic effects - Doppler terms, gravitational redshift, lensing magnification, and potential evolution - leave significant imprints in the clustering of galaxies. These signatures represent unique probes of spacetime that are inaccessible to standard Newtonian analyses but increasingly important as survey volumes grow. We outline the scientific potential of next-generation facilities, such as those envisioned within ESO's Expanding Horizons programme, to deliver the first robust measurements of relativistic effects in large-scale structure through multi-tracer power spectra and the single-tracer bispectrum of high-redshift Lyman-break galaxies. Detecting these contributions would open a new window on gravity, enabling precision tests of general relativity and its alternatives on cosmological scales in the 2040s.