Abstract
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.
Highlights
ArXiv ePrint: 2003.10114 is called the large-scale structure biasing
The key component of the bias expansion is the concept of the scale separation, where small and large scale fluctuations are separated in the sense of effective field theories
There are many other papers featuring comparable bias expansion, but given that these should all be equivalent to the frameworks chosen above, we restrict our comparative study to these three. Note that in these previous formalisms, one needs to know the non-linear dynamics of matter fluctuation to derive bias expansions, and their results were presented with the use of the standard perturbation theory (SPT) in the Einstein-de Sitter (EdS) Universe, whereas our monkey framework relaxes this assumption
Summary
The role of biasing is to connect the underlying dynamics of gravitational evolution and structure formation of dark matter to the distribution of biased tracers, like galaxies. Lagrangian perturbation theory expansion of displacement field is used to evolve the biased tracer field These two schemes are shown in Figure. and can represent all of the currently existing approaches to describing the connection of dark matter dynamics and the evolution of biased tracers. Given that the gravitational interaction is dominant on large scales, a suitable model assumes that only density fields of cold dark matter and baryons contribute to the Poisson equation:. The source terms for biased tracers, Sδ, Su, can depend on their own field δh and velocity uh, the long fields of dark matter δm that drive the dynamics on large scales as well as on the small scale physics that is characterized by some typical R∗ scale. In cases when this holds, this fact is reflected in the values of the bias coefficients indicating the level of correlation of dense dark matter region and the tracers at hand
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