Lagrangian Formulation of the Eulerian-EFT

TL;DR

This paper reformulates the Eulerian Effective Field Theory of Large Scale Structure to analyze counter terms, revealing that many have negligible time dependence and identifying six new parameters for two-loop power spectrum calculations.

Contribution

It introduces a displacement-based formulation of the EFT, clarifies the role of counter terms, and explicitly derives six new relevant parameters for advanced power spectrum modeling.

Findings

Time dependence of counter terms often negligible

Six new parameters identified for two-loop calculations

Explicit expressions for counter terms provided

Abstract

We study the counter terms in the Eulerian version of the EFT of Large Scale Structure. We reformulate the equations to solve for the displacement of fluid elements as a bookkeeping variable and study the structure of the counter terms in this formulation. We show that in many cases the time dependence of the amplitude of the counter terms is irrelevant, as solutions obtained for various time dependences differ by terms that can be reabsorbed by higher order counter terms. We show that including all effects due to the non-locality in time and the time dependence of the counter terms there are six new parameters relevant for the two loop power spectrum calculation. We give explicit expressions for all these terms and study the contributions to them from large and small modes. We show that the shape of all these terms is very similar.