DUCA: Dynamic Universe Cosmological Analysis

II. The impact of clustering dark energy on the halo mass function

¹ INAF – Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy
² INFN – Sezione di Trieste, Via Valerio 2, 34127 Trieste TS, Italy
³ IFPU – Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy
⁴ ICSC – Via Magnanelli 2, Bologna, Italy
⁵ Dipartimento di Fisica – Sezione di Astronomia, Università di Trieste, Via Tiepolo 11, Trieste 34131, Italy
⁶ Department of Astrophysics – University of Zurich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
⁷ Departamento de Física, Universidade Federal do Espírito Santo, 29075-910 Vitória, ES, Brazil
⁸ Escola de Ciências e Tecnologia, Universidade Federal do Rio Grande do Norte, Campus Universitário Lagoa Nova, 59078-970 Natal, RN, Brazil
⁹ Université Paris-Saclay, CNRS, Institut d’Astrophysique Spatiale, 91405 Orsay, France

^⋆ Corresponding author: tiago.batalha@inaf.it

Received: 6 May 2025
Accepted: 26 August 2025

Abstract

Context. 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 assumed either a homogeneous DE component or a fixed sound speed of unity, which strongly suppresses DE perturbations.

Aims. We extended the HMF calibration to clustering dark energy (CDE) models by allowing for a sound speed (c_s) value different than unity. This generalization enables a broader description of the impact of DE perturbations on structure formation.

Methods. Our approach builds upon the DUCA simulation suite, which 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 nonhomogeneous case at the turnaround. The model depends on one single parameter, which we calibrated using N-body simulations following a Bayesian approach.

Results. The resulting HMF model achieves sub-percent accuracy over a wide range of c_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_s.

Conclusions. Our results underscore the need for more precise modeling of CDE’s nonlinear regime. Numerical simulations and theoretical approaches must be advanced to fully capture the complex interplay between DE perturbations and matter.