Amending the halo model to satisfy cosmological conservation laws

TL;DR

This paper introduces an amended halo model that explicitly enforces mass and momentum conservation laws, improving the accuracy of large-scale structure predictions in cosmology.

Contribution

It presents a new framework separating linear perturbations from compensated halo profiles to ensure conservation laws are satisfied in the halo model.

Findings

Reduces overprediction of weak lensing power spectrum by over 8% on large scales.

Provides a fitting function for compensated halo profiles.

Enhances the physical accuracy of structure formation modeling.

Abstract

One of the most powerful tools in the arsenal of theoretical cosmologists is the halo model of large scale structure, which provides a phenomenological description of nonlinear structure in our universe. However, it is well known that there is no simple way to impose conservation laws in the halo model. This can severely impair the predictions on large scales for observables such as weak lensing or the kinematic Sunyaev-Zel'dovich effect, which should satisfy mass and momentum conservations, respectively. For example, the standard halo model overpredicts weak lensing power spectrum by $> 8\%$ on scales $>20$ degrees. To address this problem, we present an $Amended ~ Halo ~ Model$, explicitly separating the linear perturbations from $compensated$ halo profiles. This is guaranteed to respect conservation laws, as well as linear theory predictions on large scales. We then provide a simple fitting function for the compensated halo profiles, and discuss the modified predictions for 1-halo and 2-halo terms, as well as other cosmological observations such weak lensing power spectrum. Furthermore, we argue that the amended halo model provides a more accurate framework to capture physical effects that happen in the process of cosmological structure formation.