Integrated Perturbation Theory and One-loop Power Spectra of Biased Tracers

TL;DR

This paper derives comprehensive one-loop power spectra and correlation functions for biased tracers using integrated perturbation theory, accounting for nonlocal bias, redshift-space distortions, and primordial non-Gaussianity, advancing cosmological modeling accuracy.

Contribution

It introduces new analytic formulas for auto and cross power spectra of biased tracers, including nonlocal bias and primordial non-Gaussianity, with a fundamentally different derivation method from previous work.

Findings

Derived explicit one-loop power spectra formulas for biased tracers.

Included effects of nonlocal Lagrangian bias and primordial non-Gaussianity.

Clarified relations to recent nonlinear perturbation theory methods.

Abstract

General and explicit predictions from the integrated perturbation theory (iPT) for power spectra and correlation functions of biased tracers are derived and presented in the one-loop approximation. The iPT is a general framework of the nonlinear perturbation theory of cosmological density fields in presence of nonlocal bias, redshift-space distortions, and primordial non-Gaussianity. Analytic formulas of auto and cross power spectra of nonlocally biased tracers in both real and redshift spaces are derived and the results are comprehensively summarized. The main difference from previous formulas derived by the present author is to include effects of generally nonlocal Lagrangian bias and primordial non-Gaussianity, and the derivation method of the new formula is fundamentally different from the previous one. Relations to recent work on improved methods of nonlinear perturbation theory in literature are clarified and discussed.