Year: 2013
Type: article
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 ${\ensuremath{\delta}}_{L}$ coarse-grained on a scale ${R}_{L}$. In the latter case, the predicted tracer correlation function receives contributions of order $⟨{\ensuremath{\delta}}_{L}^{n}⟩$ 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 $\ensuremath{\propto}{k}^{2}$ 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.
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
Awards: G1390571956, G3561758408, G3815726687, G5780980149, G8493109902, THE COSMIC MICROWAVE BACKGROUND (CMB) HAS PROVIDED PRECISE CONSTRAINTS TO COSMOLOGICAL PARAMETERS AND INFLATIONARY MODELS. A VIGOROUS ONGOING PROGRAM, Fe and C rich melting and redox equilibria in the deep Earth – from Fe(II)-disproportionation to banded iron formation recycling, experiments from 3 to 40 GPa, THEORETICAL PARTICLE ASTROPHYSICS
OpenAlex ID: W2049547388