Beyond general relativity: probing gravity with gravitational redshifts

Despite the success of general relativity (GR), the unexplained nature of dark energy on cosmological scales leaves open the question of whether GR provides a complete description of gravity. This quest is further motivated by growing tensions among cosmological observations when interpreted within $Λ$CDM. Gravitational redshifts of cluster member galaxies probe cluster potentials on megaparsec scales directly, complementing conventional large-scale structure tests. Here, we investigate how redshift precision and survey design propagate into constraints on modified gravity using an end-to-end pipeline run on mock catalogues, focusing on mis-centring and spectroscopic completeness. We find that competitive measurements require wide-field spectroscopic cluster surveys explicitly designed to maximise the number of spectroscopically confirmed members per cluster, to enable high-purity stacking, and to control systematic effects.

💡 Research Summary

This white paper, titled “Beyond general relativity: probing gravity with gravitational redshifts,” presents a comprehensive analysis of using the gravitational redshift of galaxies within clusters as a direct probe for testing theories of gravity on megaparsec scales. While General Relativity (GR) remains robust locally, unexplained cosmological phenomena like dark energy and growing observational tensions motivate the search for potential modifications. The gravitational redshift effect, a direct consequence of photons climbing out of a gravitational potential, offers a complementary method to traditional large-scale structure probes, as it can be modeled in some modified gravity theories as a simple rescaling of the gravitational constant.

The core challenge identified is the weakness of the signal (~10 km/s), which necessitates stacking large ensembles of clusters to achieve a detectable statistical signal. The precision of such a measurement is critically limited by two key systematic effects: the accuracy of the cluster centre determination (mis-centring) and the spectroscopic completeness of confirmed member galaxies. The authors employ an end-to-end pipeline on mock catalogues to investigate how survey design and redshift precision propagate into constraints on a modified gravity parameter (α).

The paper reviews the current and near-future observational landscape. Current data, like from SDSS, provide a foundation but are limited. Upcoming Stage-IV facilities (e.g., Rubin LSST, Euclid, DESI) in the 2030s will photometrically detect vast numbers of clusters but are not designed to deliver the homogeneous, high-completeness spectroscopy for member galaxies required for optimal stacking. The analysis further examines the potential of Integral Field Spectroscopy (IFS) for follow-up, concluding that while valuable for detailed studies, IFS alone cannot sufficiently calibrate mis-centring due to contamination from galaxy peculiar velocities.

A pivotal insight is the distinction between “galaxy-centric” and “cluster-centric” survey strategies. Most planned 2030s spectroscopic surveys are optimized for galaxy-based cosmology (e.g., Baryon Acoustic Oscillations), leading to incidental, inhomogeneous, and often sparse sampling of cluster members. This fundamentally limits their ability to control systematics for gravitational redshift measurements. In contrast, the paper highlights the proposed Wide-Field Spectroscopic Telescope (WST) for the 2040s as a paradigm shift. WST is conceived with an explicit cluster program, using its high-multiplex and wide-field capabilities to uniformly and deeply sample cluster cores and outskirts, building a high-purity spectroscopic cluster catalogue.

Simulations comparing different completeness scenarios demonstrate that a dedicated cluster-survey setup can significantly reduce error bars, particularly in the cluster outskirts, compared to a galaxy-survey-like strategy. The paper concludes that while 2030s facilities will enable the first generation of precision stacked gravitational redshift measurements, their constraints will be limited by the inherent systematics of galaxy-centric surveys. To fully exploit this probe and achieve transformative constraints on gravity, a dedicated, cluster-optimized facility like WST is deemed essential. The authors also stress the need for parallel advancements in theoretical modeling to explore different parameterizations of gravity beyond the simple α-model used in their analysis.