  We present a new analytic approach to describe large scale structure
formation in the mildly non-linear regime. The central object of the method is
the time-dependent probability distribution function generating correlators of
the cosmological observables at a given moment of time. Expanding the
distribution function around the Gaussian weight we formulate a perturbative
technique to calculate non-linear corrections to cosmological correlators,
similar to the diagrammatic expansion in a three-dimensional Euclidean quantum
field theory, with time playing the role of an external parameter. For the
physically relevant case of cold dark matter in an Einstein--de Sitter
universe, the time evolution of the distribution function can be found exactly
and is encapsulated by a time-dependent coupling constant controlling the
perturbative expansion. We show that all building blocks of the expansion are
free from spurious infrared enhanced contributions that plague the standard
cosmological perturbation theory. This paves the way towards the systematic
resummation of infrared effects in large scale structure formation. We also
argue that the approach proposed here provides a natural framework to account
for the influence of short-scale dynamics on larger scales along the lines of
effective field theory.
