Forecasting constraints on the cosmic duality relation with galaxy clusters

One of the fundamental hypotheses in observational cosmology is the validity of the so-called cosmic distance-duality relation. In this paper, we perform Monte Carlo simulations based on the method developed in Holanda, Goncalves, and Alcaniz [J. Cosmol. Astropart. Phys. 06 (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 amount of data would be already close to the required number to check the validity of the cosmic distance-duality relation at 2 sigma.