The EFT likelihood for large-scale structure in redshift space

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