DUCA: Dynamic Universe Cosmological Analysis

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 (cs) 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 cs 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 cs. 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.