Redshift Space Distortions in the Effective Field Theory of Large Scale Structures

TL;DR

This paper develops a formalism within the Effective Field Theory framework to accurately model redshift space distortions in large-scale structure, accounting for non-perturbative effects and introducing new counterterms for improved predictions.

Contribution

It extends the EFTofLSS to include redshift space distortions, deriving new expressions and counterterms, and generalizes IR resummation techniques for this context.

Findings

Introduces a formalism valid for dark matter and collapsed objects.

Identifies additional counterterms needed in redshift space.

Generalizes IR resummation to redshift space distortions.

Abstract

We introduce a formalism, valid both for dark matter and collapsed objects, that allows us to describe redshift space distortions in the context of the Effective Field Theory of Large Scale Structures (EFTofLSS). Expressing density perturbations in redshift space corresponds to performing a change of coordinates and the resulting expressions contain products of density perturbations and velocity fields evaluated at the same location. These terms are sensitive to non-perturbative short-distance physics and in order to correctly treat them they need to be renormalized by adding suitable counterterms. Therefore more counterterms are required in redshift space expressions compared to their real space analogs. In particular in the expression for the one-loop matter power spectrum there are two new counterterms. Just as in real space, long wavelength displacements affect correlation functions in redshift space and need to be resummed. We generalize the real space formulas for IR resummation to this case: the final expressions are conceptually similar but are more challenging to compute numerically due to their reduced symmetry.