A Model for the Redshift-Space Galaxy 4-Point Correlation Function

TL;DR

This paper develops a theoretical model for the galaxy 4-point correlation function in redshift space, incorporating nonlinear gravitational effects and redshift distortions, to improve cosmological parameter constraints from upcoming galaxy surveys.

Contribution

It provides the first tree-level, nonlinear, redshift-space galaxy 4PCF model based on the trispectrum, enabling better analysis of survey data and cosmological constraints.

Findings

Model captures nonlinear gravitational effects in 4PCF

Enables use of BAO features to constrain expansion history

Facilitates galaxy bias parameter estimation

Abstract

The field of cosmology is entering an epoch of unparalleled wealth of observational data thanks to galaxy surveys such as DESI, Euclid, and Roman. Therefore, it is essential to have a firm theoretical basis that allows the effective analysis of the data. With this purpose, we compute the nonlinear, gravitationally-induced connected galaxy 4-point correlation function (4PCF) at the tree level in Standard Perturbation Theory (SPT), including redshift-space distortions (RSD). We begin from the trispectrum and take its inverse Fourier transform into configuration space, exploiting the isotropic basis functions of Cahn & Slepian (2023). We ultimately reduce the configuration-space expression to low-dimensional radial integrals of the power spectrum. This model will enable the use of the BAO feature in the connected 4PCF to sharpen our constraints on the expansion history of the Universe. It will also offer an additional avenue for determining the galaxy bias parameters, and thus tighten our cosmological constraints by breaking degeneracies. Survey geometry can be corrected in the 4PCF, and many systematics are localized, which is an advantage over data analysis with the trispectrum.