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Probing General Relativity on Cosmological Scales in the 2040s

Federico Montano, Samantha J. Rossiter, Chris Addis, Jessie Hammond, Stefano Camera, Chris Clarkson, Mohamed Yousry Elkhashab, Massimo Guidi, Ofer Lahav, Giovanni Aricò, Sofia Contarini, Pratika Dayal, Giulia Degni, Antonio Farina, Vid Iršič, Federico Marulli, Elena Sarpa, Simone Sartori, Emiliano Sefusatti, Francesco Verdiani, Giovanni Verza

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.

Probing General Relativity on Cosmological Scales in the 2040s

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.
Paper Structure (3 sections, 2 figures)

This paper contains 3 sections, 2 figures.

Table of Contents

  1. Relativistic effects in the large-scale structure of the universe
  2. Observational status
  3. Technology requirements

Figures (2)

  • Figure 1: Monopole (top) of the 3D power spectrum for a bright galaxy sample (BGS, $m_{\rm c}=20$), an H$\alpha$ ($F_{\rm c} = 2 \times 10^{-16} \, {\rm erg\,cm^{-2}\,s^{-1}}$) and a Lyman-break galaxy (LBG, $m_{\rm c} = 25$) survey and the dipole contribution (bottom) for a bright-faint split cross-power spectrum, in units of $(\mathrm{Mpc}/h)^{3}$. Evaluated using https://github.com/craddis1/CosmoWAP, the total signal (T) is decomposed into its main components: standard (S, i.e. Newtonian), local GR projection effects (LP), and integrated GR terms (I).
  • Figure 2: Estimate of SNR of local relativistic effects in a LBG population (modelled as in 2019WilsonWhite, in $z\in[2,\,5]$), assuming a WST-like 2024WST_ redshift survey, with a conservative sky coverage of $10\,00 \;\rm deg^2$. Left: Colourmap of the SNR in a faint-bright multi-tracer full-power spectrum measurement, $P(k,\,\mu),$ with $\mu\in[0,\,1]$, as a function of magnitude cut and split 2024MontanoCamera. Right: Total SNR in an auto-bispectrum analysis; deeper cuts yield higher significance 2025Rossiter_.