Measuring Cosmological Distances Using Cluster Edges as a Standard Ruler

TL;DR

This paper proposes a new method using galaxy cluster edges as a standard ruler to measure cosmological distances, enabling precise determination of the Hubble constant with current and upcoming survey data.

Contribution

It introduces a novel approach to measure cosmological distances by utilizing the velocity dispersion kink in galaxy clusters as a gravity-calibrated standard ruler.

Findings

SDSS data can measure Hubble constant with 3% precision

DESI data can achieve 1.3% precision on Hubble constant

Supernova data can improve DESI measurement to 0.7%

Abstract

The line-of-sight velocity dispersion profile of galaxy clusters exhibits a "kink" corresponding to the spatial extent of orbiting galaxies. Because the spatial extent of a cluster is correlated with the amplitude of the velocity dispersion profile, we can utilise this feature as a gravity-calibrated standard ruler. Specifically, the amplitude of the velocity dispersion data allows us to infer the physical cluster size. Consequently, observations of the angular scale of the "kink" in the profile can be translated into a distance measurement to the cluster. Assuming the relation between cluster radius and cluster velocity dispersion can be calibrated from simulations, we forecast that with existing data from the Sloan Digital Sky Survey (SDSS) we will be able to measure the Hubble constant with $3\%$ precision. Implementing our method with data from the Dark Energy Spectroscopic Instrument (DESI) will result in a $1.3\%$ measurement of the Hubble constant. Adding cosmological supernova data improves the uncertainty of the DESI measurement to $0.7\%$.