Cluster gravitational redshifts: uncertainties and survey requirements

Authors: Eleni Tsaprazi, Giorgio F. Lesci, Federico Marulli, Alan F. Heavens, Enrico Maraboli Date: 2026-03-26 Paper ID: openalex:2603.25339

Summary

This paper presents an end-to-end forecasting pipeline to quantify the achievable precision of cluster gravitational redshifts as a probe for modified gravity, parametrized by a linear rescaling $\alpha_{\mathrm{MG}}$. The methodology involves generating synthetic galaxy catalogues using a Halo Occupation Distribution (HOD) model, applying survey-like selections, and systematically varying observational uncertainties. The authors find that velocity dispersion imposes a hard limit on redshift precision gains and that spectroscopic surveys are preferable to photometric ones for this cosmological constraint. A critical finding is that accurate cluster centering is essential in upcoming high signal-to-noise surveys to avoid systematic biases mimicking new physics.

Key Contributions

• Established an end-to-end forecasting pipeline, combining generative modeling, HOD, and survey simulations, to assess the precision of cluster gravitational redshifts ($\alpha_{\mathrm{MG}}$) as a modified gravity probe.
• Determined that intracluster velocity dispersion sets an effective floor, with no precision improvement for $\alpha_{\mathrm{MG}}$ beyond redshift precision of $\sigma_z\sim 10^{-4}(1+z)$.
• Concluded that shallow, narrower spectroscopic surveys are more advantageous than deep, wide photometric surveys for obtaining precise constraints on modified gravity parameters.
• Identified accurate determination of cluster centres as an essential requirement for upcoming high Signal-to-Noise surveys to prevent misinterpreting systematic centering errors as new physics.

Limitations

The study focuses on forecasting pipeline sensitivity, implicitly assuming the underlying theoretical parameterization ($\alpha_{\mathrm{MG}}$) is sufficient to capture all relevant modifications to GR.’,open_questions:[],published:

Open Questions & Future Work

• exploring-post-GW170817-modified-gravity-models
• accurate-cluster-center-determination-strategies
• self-consistent-modified-gravity-simulations

Key Concepts

• cluster-gravitational-redshifts-modified-gravity-probe: Using the gravitational redshift of galaxies within galaxy clusters to constrain deviations from General Relativity (GR) via a parameter $\alpha_{\mathrm{MG}}$.
• halo-occupation-distribution-population-model: A five-parameter statistical model used to populate dark matter haloes with observable galaxies based on halo mass and other properties.

Archivist Review

Approved two core concepts: the central observable (Gravitational Redshifts as a Probe) and a key simulation component (HOD Model). For open questions, three candidates were rejected as they primarily describe general follow-up or required infrastructure development. Three remain: one on exploring viable modified gravity models post-GW170817, one on solving the critical center-determination systematic, and one on the necessity of self-consistent modified-gravity simulations, all of which represent substantial methodological or physical bottlenecks for this research program.

Approved Concepts

• Cluster Gravitational Redshifts as a Modified Gravity Probe: The entire paper focuses on establishing and quantifying the precision of this specific cosmological probe.
• Halo Occupation Distribution (HOD) Population Model: The HOD is a critical, explicit modeling component used to generate the synthetic member galaxy catalog necessary for the forecasting pipeline.

Approved Open Questions

• Investigate viable modified gravity models: The current analysis focuses on parameterizations compatible with standard modified gravity models; exploring new, viable models is necessary for a comprehensive test of modified gravity.
• Develop accurate cluster center proxies: Accurate center determination is critical because mis-centering can introduce systematic shifts that mimic deviations from GR at the level required by high-precision Stage-IV/V surveys.
• Develop self-consistent modified gravity simulations: Ignoring self-consistent structure formation in modified gravity may introduce model biases that become significant as statistical errors decrease.

Rejected Candidates

• [open_question] Exploit future spectroscopic facilities (future-survey-exploitation-gravitational-redshifts) - low_impact: This open question is essentially boilerplate future work emphasizing the use of named surveys, rather than pointing to a specific unsolved technical mechanism.
• [open_question] Explore richer gravity parameterizations (explore-comprehensive-modified-gravity-parameterizations) - low_impact: While this is a reasonable research direction, the paper suggests it as a natural follow-up rather than identifying a specific, deep, unresolved technical bottleneck in the methodology itself.
• [open_question] Propagate mass uncertainties and match survey specifics (propagate-mass-uncertainties-match-surveys) - low_impact: This summarizes general next steps in applying the pipeline (propagating calibration errors and matching survey specs) but does not isolate a unique, deep, unresolved technical challenge.

Links

• Abstract
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