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

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