Halo Mass Functions in Early Dark Energy Cosmologies

TL;DR

This paper shows that the critical density contrast for structure formation remains unaffected by early dark energy models if dark energy is homogeneous, restoring the accuracy of the Press-Schechter approach for predicting halo mass functions.

Contribution

It demonstrates that the linear density contrast at collapse is insensitive to dark energy properties in homogeneous models, correcting previous misconceptions and restoring the validity of the extended Press-Schechter method.

Findings

$ ext{delta}_c$ is insensitive to dark energy in homogeneous models

Press-Schechter approach accuracy is restored with correct $ ext{delta}_c$

Dark energy physics needed for significant $ ext{delta}_c$ change is discussed

Abstract

We examine the linear density contrast at collapse time, $\delta_c$ for large-scale structure in dynamical dark energy cosmologies, including models with early dark energy. Contrary to previous results, we find that as long as dark energy is homogeneous on small scales, $\delta_c$ is insensitive to dark energy properties for parameter values fitting current data, including the case of early dark energy. This is significant since using the correct $\delta_c$ is crucial for accurate Press-Schechter prediction of the halo mass function. Previous results have found an apparent failing of the extended Press-Schechter approach (Sheth-Tormen) for early dark energy. Our calculations demonstrate that with the correct $\delta_c$ the accuracy of this approach is restored. We discuss the significance of this result for the halo mass function and examine what dark energy physics would be needed to cause significant change in $\delta_c$, and the observational signatures this would leave.