The study of QCD’s phase diagram has drawn attention of the high energy community in the past few decades. One of its most intriguing aspects is the existence of a Critical End-point and its location. Several works have proposed possible experimental signatures of its location, but most need too many statistics to be conclusive. In this talk, I will present a study on a possible observable, called the Lévy stability index, that could signal the presence of critical phenomena and how the Equation of State of nuclear matter at high temperature and density might affect it. This Lévy stability Index can be accessed through the analysis of two-pion correlations. To this end I will show how it behaves without the presence of a critical point and the most recent progress that we have made towards its study, by taking into account the effects of a LQCD-based Equation of State with a Critical End-point