The speed of sound of nonlinear large-scale structures

The Effective Field Theory of Large Scale Structure (EFT of LSS) has found tremendous success as a perturbative framework for the evolution of large scale structure, and it is now routinely used to compare theoretical predictions against cosmological observations. The model for the total matter field includes one nuisance parameter at 1-loop order, the effective sound speed, which can be extracted by matching the EFT to full N-body simulations. In this talk we explore the foundations of EFT methods for LSS. We first show that the emergence of the sound speed can be understood even without EFT ingredients, through a perturbative framework that solves the Vlasov-Poisson system of equations directly in phase space. We then move on to discuss how one can estimate the effective sound speed, via separate universe techniques, with analytic calculations. The estimate is in good agreement with simulation results, and we show it can be used to extract the cosmology dependence of the effective sound speed and to shed light on what cosmic structures shape its value.