Nonlinear perturbation theory with halo bias and redshift-space distortions via the Lagrangian picture

TL;DR

This paper develops an analytic nonlinear perturbation theory in the Lagrangian framework to incorporate halo bias and redshift-space distortions, aiding precise galaxy survey predictions without costly simulations.

Contribution

It introduces a Lagrangian-based perturbation formalism that naturally includes local halo bias and redshift-space distortions, avoiding assumptions like spherical collapse.

Findings

Analytic one-loop corrections for halo power spectrum and correlation function in redshift space.

Weak nonlinear effects cause a smooth scale dependence in halo bias.

Baryon acoustic oscillation features are preserved despite nonlinearities.

Abstract

The nonlinear perturbation theory of gravitational instability is extended to include effects of both biasing and redshift-space distortions, which are inevitable in predicting observable quantities in galaxy surveys. The precise determination of scales of baryon acoustic oscillations is crucial to investigate the nature of dark energy by galaxy surveys. We find that a local Lagrangian bias and redshift-space distortions are naturally incorporated in our formalism of perturbation theory with a resummation technique via the Lagrangian picture. Our formalism is applicable to any biasing scheme which is local in Lagrangian space, including the halo bias as a special case. Weakly nonlinear effects on halo clustering in redshift space are analytically given.We assume only a fundamental idea of the halo model: haloes form according to the extended Press-Schechter theory, and the spatial distributions are locally biased in Lagrangian space. There is no need for assuming the spherical collapse model to follow the dynamical evolution, which is additionally assumed in standard halo prescriptions. One-loop corrections to the power spectrum and correlation function of haloes in redshift space are explicitly derived and presented. Instead of relying on expensive numerical simulations, our approach provides an analytic way of investigating the weakly nonlinear effects, simultaneously including the nonlinear biasing and nonlinear redshift-space distortions. Nonlinearity introduces a weak scale dependence in the halo bias. The scale dependence is a smooth function in Fourier space, and the bias does not critically change the feature of baryon acoustic oscillations in the power spectrum. The same feature in the correlation function is less affected by nonlinear effects of biasing.