We study the EFT likelihood for biased tracers in redshift space, for which the bias expansion of the galaxy velocity field $\mathbf{ v}_g$ plays a fundamental role. The equivalence principle forbids stochastic contributions to $\mathbf{ v}_g$ to survive at small $k$. Therefore, at leading order in derivatives the form of the likelihood ${ \cal P}[\tilde{ \delta}_g|\delta,\!\mathbf{ v}]$ to observe a redshift-space galaxy overdensity $\tilde{ \delta}_g(\tilde{ \mathbf{ x}})$ given a rest-frame matter and velocity fields $\delta(\mathbf{ x})$, $\mathbf{ v}(\mathbf{ x})$ is fixed by the rest-frame noise. If this noise is Gaussian with constant power spectrum, ${ \cal P}[\tilde{ \delta}_g|\delta,\!\mathbf{ v}]$ is also a Gaussian in the difference between $\tilde{ \delta}_g(\tilde{ \mathbf{ x}})$ and its bias expansion: redshift-space distortions only make the covariance depend on $\delta(\mathbf{ x})$ and $\mathbf{ v}(\mathbf{ x})$. 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.
Categories: astro-ph.CO astro-ph.GA