Understand
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 $\mathbf{v}(\mathbf{x})$.