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

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.

Measuring neutrino masses with large-scale structure: Euclid forecast with controlled theoretical error

“…[19,21,23,83,89,90]. We implement the IR resummation procedure developed in the context of time-sliced perturbation theory [22,24,26]. This procedure is based on rigorous power counting rules and gives an accurate estimate of the theoretical error at each order of IR resummation.…”

“…This procedure, called infrared (IR) resummation, is essential for an accurate description of the BAO and has been formulated within various theoretical frameworks [19][20][21][22][23][24][25]. We will adopt a systematic approach of [22,24] streamlined in the context of time-sliced perturbation theory [26].Second, we will use the effective field theory of large-scale structure (EFT) to account for the back-reaction of small scale nonlinearities on larger scales [17,27,28]. This approach removes the unphysical UV sensitivity of perturbation theory loop integrals and parameterizes the ignorance about short scale-dynamics by various effective operators in the equations of motion for the dark matter fluid.…”

Cosmological parameters and neutrino masses from the final Planck and full-shape BOSS data

“…The main difference with respect to previous studies is the implementation of infrared (IR) resummation and the presence of the so-called "counterterms." IR resummation describes the non-linear evolution of baryon acoustic oscillations, which was independently formulated within several different but equivalent frameworks [35][36][37][38][39][40][41]. The major novelties compared to the previous models are: (i) The non-linear damping applies only to the oscillating ("wiggly") part of the matter power spectrum, (ii) It does not require any fitting parameters, and (iii) It includes corrections beyond the commonly used exponential suppression.…”

The EFT likelihood for large-scale structure

“…in the smallness of δ on large scales) and the expansion in derivatives. Finally, as we will see at the end of the paper, the method employed here easily allows to include the impact of primordial non-Gaussianity.Before proceeding to the main body of the paper, we emphasize that functional methods feature prominently also in [14,15]. In these two papers the authors develop, roughly speaking, an analytic approach to compute correlators of δ by deriving an evolution equation for P[δ], the likelihood of the nonlinear matter field.Their approach and the one followed in this paper have some overlap.…”