Magíster en Ciencias, Mención Astronomía / Cold Dark matter (ΛCDM) models have been remarkably successful to explain the observed large scale structure of our universe on scales of the order of galaxy clusters (≥ 4 Mpc) and above (therefore in this work we consider large scale beyond the aforementioned limit). However, this class of models has some problems at short scales, (∼ 1 Mpc or lower) dubbed Small Scale Controversies . It is important to remark that, for purposes of our work, we consider lower than 1 Mpc as short-scales. One of small scale issues is associated to the Dark Matter halo structure: cosmological simulations that take into account only gravity and collisionless matter, predict halos and substructures with densities much higher than those derived from galactic dynamics and observations. A possible way to conciliate theory with observations is to consider self interactive dark matter (SIDM). Models with SIDM generate predictions consistent with observations on Large Scales, the domain where ΛCDM is successful, but in addition it does not conflict with observations on "small scale". In absence of a theory that incorporates self interactive dark matter, it is possible to use the so-called Effective Field Theory (EFT) framework to investigate some aspects of dark matter. The use of effective field theory techniques to study the role of dark matter during the period of structure formation in the Universe has provided a powerful parametrization of the dark matter physics at short scales. Recently, some researchers have advocated the use of the latter approach to model the large scale structure as a fluid and considering gravity by incorporating systematically non linear terms in the theoretical treatment. In this work, we use some recent approaches [2, 12] to study analytically collisional dark matter in the form of self interactions. We derive generalized expressions of some of the equations presented in ref.[2], corresponding to corrections to the momentum equation and the effective energy equation, and discuss the implications for the behavior of dark matter and its effect on structure formation. In particular, we find that, by taking into account self interactions, some corrections terms appear both in the momentum and energy equations. These corrections arise from the non-linear effects that modify the standard equations. We show that these new terms can solve some of the small scale issues because the self interactive dark matter reduces the central densities of the galaxy dark matter halos.