Time-Sliced Perturbation Theory for Large Scale Structure I: General Formalism

TL;DR

This paper introduces a novel analytic framework based on time-sliced perturbation theory to model large scale structure formation in the mildly non-linear regime, avoiding infrared issues and enabling systematic resummation.

Contribution

It develops a new perturbative approach using a time-dependent probability distribution function, providing a systematic way to include non-linear corrections and infrared resummation in large scale structure modeling.

Findings

Exact time evolution of the distribution function for Einstein--de Sitter universe

Infrared divergences are absent in the new expansion

Framework naturally incorporates short-scale effects via effective field theory

Abstract

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.