In this talk I'’ll introduce time-sliced perturbation theory (TSPT) a method to study the mildly non-linear regime of large scale structure. TSPT concentrates in the evolution of the probability distribution function for cosmological fields, which has certain advantages with respect to the standard approach. I will focus on one of them: in contrast to the standard approach, TSPT is automatically Galilean invariant (a symmetry of the full solution). This allows for the first systematic treatment of the non-linear evolution of baryonic acoustic oscillations (a key observable in large scale structure). If time permits, I'’ll comment on how the formalism allows to describe the impact of small scales at large scales in the language of Wilsonian RG flow.