DUCA: Dynamic Universe Cosmological Analysis. II. The impact of clustering dark energy on the halo mass function

TL;DR

This paper extends the calibration of the halo mass function to clustering dark energy models with variable sound speed, achieving high accuracy and revealing nuanced impacts on structure formation, especially in non-phantom scenarios.

Contribution

It introduces a new HMF calibration method for clustering dark energy with arbitrary sound speed, calibrated with N-body simulations, improving modeling accuracy.

Findings

HMF calibration achieves sub-percent accuracy across sound speeds.

CDE effects on halo abundance are modest but more significant in non-phantom models.

Lower impact predicted for low sound speed compared to spherical collapse models.

Abstract

Galaxy clusters are powerful probes of cosmology, and the halo mass function (HMF) serves as a fundamental tool for extracting cosmological information. Previous calibrations of the HMF in dynamical dark energy (DE) models either assumed a homogeneous DE component or a fixed sound speed of unity, which strongly suppresses DE perturbations. We extend the HMF calibration to clustering dark energy (CDE) models by allowing for a sound speed $(c_{\rm s})$ value different than unity. This generalization enables a broader description of the impact of DE perturbations on structure formation. Our approach builds upon the DUCA simulation suite that accounts for DE at the background and perturbative levels. We present an HMF calibration based on introducing an effective peak height while maintaining the multiplicity function as previously calibrated. The effective peak height is written as a function of the peak height computed using the matter power spectrum of the homogeneous DE case, but it is modulated by the amplitude of DE and matter perturbations on the non-homogeneous case at the turnaround. The model depends on one single parameter, which we calibrate using $N$-body simulations, following a Bayesian approach. The resulting HMF model achieves sub-percent accuracy over a wide range of $c_{\rm s}$ values. Our analysis reveals that, although the overall impact of CDE on halo abundances remains modest (typically a few percent), the effects are more pronounced in non-phantom DE scenarios. Our model qualitatively agrees with predictions based on the spherical collapse model, but predicts a significantly lower impact for low $c_{\rm s}$. Our results underscore the need for more precise modeling of CDE's nonlinear regime. Numerical simulations and theoretical approaches must be advanced to capture the complex interplay between DE perturbations and matter fully.