Cluster gravitational redshifts: uncertainties and survey requirements

Abstract

We investigate the impact of observational and theoretical uncertainties in cluster gravitational redshifts as a probe of modified gravity using an end-to-end forecasting pipeline. We use a generative model to build a halo catalogue with $M_{500}\ge 3\times 10^{13}{M}_{\odot }$, populate haloes with member galaxies via a five-parameter halo occupation distribution (HOD), assign projected positions from radial density profiles, apply survey-like selections, and infer a linear rescaling of the gravitational potential, ${\alpha }_{\mathrm{MG}}$, to parameterise modifications to general relativity (GR). We vary redshift uncertainties, radial and mass-redshift completeness, member abundance, minimum mass and maximum redshift, as well as mis-specify the clusters density and velocity profiles, centres, and mass function. We find that the intracluster velocity dispersion sets an effective floor: improving redshift precision beyond ${\sigma }_z\sim 10^{-4}(1+z)$ brings no improvement in the precision of ${\alpha }_{\mathrm{MG}}$. Realistic redshift and mass cuts primarily remove low-mass haloes and have minimal impact on the ${\alpha }_{\mathrm{MG}}$ precision. In this setting, we find that shallow, narrower spectroscopic surveys are preferable to deep, wide photometric ones for precise modified gravity constraints. We further find that mis-centring can mimic significant departures from GR. Baryonic deviations from a Navarro-Frenk-White profile and velocity anisotropies do not introduce appreciable biases. In the high-S/N regime of upcoming surveys, accurate determination of cluster centres will be essential to avoid interpreting systematic effects as new physics. The Spectroscopic Stage-5 Experiment and the Widefield Spectroscopic Telescope provide a clear route toward establishing gravitational redshifts as a competitive probe of modified gravity.

arXiv comment13 pages, 5 figures, accepted by MNRAS

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