Time-sliced perturbation theory for large scale structure I: general formalism

Abstract

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