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 (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.