The EFT likelihood for large-scale structure in redshift space

Abstract

We study the EFT likelihood for biased tracers in redshift space, for which the bias expansion of the galaxy velocity field v⃗g plays a fundamental role. The equivalence principle forbids stochastic contributions to v⃗g to survive at small k. Therefore, at leading order in derivatives the form of the likelihood \U0001d4ab[̃δg|δ,v⃗] to observe a redshift-space galaxy overdensity ̃δg(̃x⃗) given a rest-frame matter and velocity fields δ(x⃗), v⃗(x⃗) is fixed by the rest-frame noise. If this noise is Gaussian with constant power spectrum, \U0001d4ab[̃δg|δ,v⃗] is also a Gaussian in the difference between ̃δg(̃x⃗) and its bias expansion: redshift-space distortions only make the covariance depend on δ(x⃗) and v⃗(x⃗). We then show how to match this result to perturbation theory, and that one can consistently neglect the field-dependent covariance if the bias expansion is stopped at second order in perturbations. We discuss qualitatively how this affects numerical implementations of the EFT-based forward modeling, and how the picture changes when the survey window function is taken into account.