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

TL;DR

The paper tackles redshift-space distortions within the EFTofLSS, showing that mapping to redshift space introduces UV-sensitive products of density and velocity that must be renormalized. The authors provide a one-loop redshift-space power spectrum with two new counterterms $(1+f\mu^2)\mu^2 (k/k_{\rm NL})^2 P_{\delta\delta,11}$ and $(1+f\mu^2)\mu^4 (k/k_{\rm NL})^2 P_{\delta\delta,11}$ and generalize IR resummation to redshift space via a Lagrangian framework using the transformed momentum $\vec{\tilde{k}}=B\vec{k}$ with $B=\mathrm{diag}(1,1,1+f)$. The work also extends to biased tracers, introducing an additional contact operator renormalization and providing practical, IR-safe expressions for the redshift-space power spectrum. This framework enables accurate modeling of BAO and large-scale clustering in redshift surveys and paves the way for data-driven cosmological parameter estimation.

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.