Abstract
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 coarse-grained on a scale . In the latter case, the predicted tracer correlation function receives contributions of order at each perturbative order , 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 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.
- Received 7 January 2013
DOI:https://doi.org/10.1103/PhysRevD.88.023515
© 2013 American Physical Society