The Ly$\alpha$ forest flux correlation function: a perturbation theory perspective

TL;DR

This paper develops a perturbation theory framework to understand the large-scale correlations in the Lyα forest flux, linking observable flux statistics to matter fluctuations and addressing complex small-scale physics effects.

Contribution

It introduces a systematic perturbation theory approach to model Lyα forest flux correlations, including bias expansion and renormalization of bias coefficients.

Findings

Large-scale flux power spectrum is proportional to the linear matter power spectrum.

Both isotropic and anisotropic flux components are influenced by small-scale physics.

The framework connects flux correlations directly to matter fluctuation statistics.

Abstract

The Ly$\alpha$ forest provides one of the best means of mapping large-scale structure at high redshift, including our tightest constraint on the distance-redshift relation before cosmic noon. We describe how the large-scale correlations in the Ly$\alpha$ forest can be understood as an expansion in cumulants of the optical depth field, which itself can be related to the density field by a bias expansion. This provides a direct connection between the observable and the statistics of the matter fluctuations which can be computed in a systematic manner. We discuss the way in which complex, small-scale physics enters the predictions, the origin of the much-discussed velocity bias and the `renormalization' of the large-scale bias coefficients. Our calculations are within the context of perturbation theory, but we also make contact with earlier work using the peak-background split. Using the structure of the equations of motion we demonstrate, to all orders in perturbation theory, that the large-scale flux power spectrum becomes the linear spectrum times the square of a quadratic in the cosine of the angle to the line of sight. Unlike the case of galaxies, both the isotropic and anisotropic pieces receive contributions from small-scale physics.