2012/12/31 by Fabian Schmidt, Donghui Jeong, Vincent Desjacques · 1 citation
Physics and Astronomy · #astro-ph.CO
paper · pdf · doi:10.1103/physrevd.88.023515
25 pages, 1 figure, 1 table; v2: expanded on case of univ. mass functions (Sec II C) and connection to multipoint propagators; v3: minor edits and clarifications, matches PRD published version
arxiv created 2013/07/03 · arxiv updated 2013/08/09
We present a derivation of two-point correlations of general tracers in the peak-background split (PBS) framework by way of a rigorous definition of the PBS argument. Our expressions only depend on connected matter correlators and "renormalized" bias parameters with clear physical interpretation, and are independent of any coarse-graining scale. This result should be contrasted with the naive expression derived from a local bias expansion of the tracer number density with respect to the matter density perturbation δL coarse-grained on a scale RL. In the latter case, the predicted tracer correlation function receives contributions of order <δLn> at each perturbative order n, whereas, in our formalism, these are absorbed in the PBS bias parameters at all orders. Further, this approach naturally predicts both a scale-dependent bias ~ k2 such as found for peaks of the density field, and the scale-dependent bias induced by primordial non-Gaussianity in the initial conditions. The only assumption made about the tracers is that their abundance at a given position depends solely on the matter distribution within a finite region around that position.