Forecasting constraints on the cosmic duality relation with galaxy clusters

TL;DR

This paper uses Monte Carlo simulations to determine how many galaxy cluster observations are needed to test the cosmic distance-duality relation's validity at specific confidence levels, highlighting the importance of reducing observational uncertainties.

Contribution

It introduces a simulation-based method to estimate the required number of galaxy cluster observations for testing the cosmic duality relation at given confidence levels.

Findings

Current data are insufficient to test the relation at 2σ confidence.

Reducing observational uncertainties by half makes existing data sufficient for validation.

The required number of observations increases significantly with current uncertainties.

Abstract

One of the fundamental hypotheses in observational cosmology is the validity of the so-called cosmic distance-duality relation (CDDR). In this paper, we perform Monte Carlo simulations based on the method developed in Holanda, Goncalves & Alcaniz (2012) [JCAP 1206 (2012) 022] to answer the following question: what is the number of galaxy clusters observations N_{crit} needed to check the validity of this relation at a given confidence level? At 2\sigma, we find that N_{crit} should be increased at least by a factor of 5 relative to the current sample size if we assume the current observational uncertainty \sigma_{obs}. Reducing this latter quantity by a factor of 2, we show that the present number of data would be already enough to check the validity of the CDDR at 2\sigma.