Perturbative description of bias tracers using consistency relations of LSS

We develop a simple formalism of biased tracers that we dub Monkey bias. In this formalism, a biased tracer field is constructed directly in terms of the linear matter fluctuation field and the set of derivative operators acting on it. Such bias expansion is first organized based on the general structure of non-linear dynamical equations for the biased tracers. Further physical conditions, like the equivalence principle, are imposed on tree-level correlators utilising the consistency relations. We obtain the bias expansion up to the third-order in linear matter fluctuation in the generalized ΛCDM background, which reproduces the previous results in the limit of the EdS universe. This algorithmic construction of our bias operator basis is well suited for extensions towards higher-order bias fields. Moreover, this formalism reveals that biased tracer dynamics in generalized ΛCDM background is not entirely degenerate with the rest of bias parameters, thus opening a possibility of testing the background cosmology through the observations of biased tracers.