Halo Mass Functions in Early Dark Energy Cosmologies

Abstract

We examine the linear density contrast at collapse time, $δ_c$ 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, $δ_c$ 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 $δ_c$ 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 $δ_c$ 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 $δ_c$, and the observational signatures this would leave.