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

TL;DR

This paper extends halo mass function calibrations to clustering dark energy by enabling a general DE sound speed $c_{ m s}$ and using the DUCA $N$-body simulations to capture background and perturbative DE effects. It introduces an effective peak height to map linear theory to nonlinear halo abundances in CDE cosmologies and calibrates this with a Bayesian framework, achieving sub-percent accuracy across a range of $c_{ m s}$ values. The study finds modest overall changes in halo counts (typically a few percent), larger impacts for non-phantom DE, and that linear predictions overestimate nonlinear effects by about a factor of two, necessitating the empirical modification. The results stress the continued need for advanced nonlinear modeling of DE perturbations and careful consideration of DE microphysics when interpreting cluster abundances in future surveys. Overall, the work provides a robust, sub-percent-accurate framework for incorporating DE clustering into HMF predictions relevant to upcoming large-scale structure data.

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.

Figures (7)

• Figure 1: Relative differences in HMF at redshift zero for varying DE sound speeds $c_{\rm s}^2$, normalized to the reference case $c_{\rm s}^2=1$. Different colors correspond to different DE EOS parameters, while different panels correspond to different sound speeds. From left to right, $c_{\rm s}^2$ is $10^{-7}$, $10^{-5}$, and $10^{-3}$. Gray bands mark $\pm 1 \%$ (dark) and $\pm 2 \%$ (light) differences.
• Figure 2: DE power spectrum at redshift zero and sound speeds $c_{\rm s}^2=10^{-7}$ and $c_{\rm s}^2=10^{-7}$ for the different DE EOS parameters.
• Figure 3: Relative differences in the halo mass function (HMF) at $z = 0$ for the case where $c_{\rm s}^2 = 10^{-7}$, compared to the reference case $c_{\rm s}^2 = 1$, for different DE EOS parameters (filled lines in different colors). The figure also shows the prediction of this quantity from our baseline model, presented in Paper I, as indicated by the dotted lines.
• Figure 4: The density fields in a comoving volume of size 1 Gpc$/h$ at $z=0$. The left panel shows the matter distribution for the simulation #3, i.e., $w_0 = -0.8,\, w_a = 0.1$. The middle and right panels show the DE distributions for the same simulation and its phantom twin $(w_0 = -1.2,\, w_a = -0.1)$, respectively. The region inside the red rectangles is zoomed and displayed in an inset at the lower right.
• Figure 5: Comparison between the model calibrated on the Simulations 1--12 using the PPF description presented in Table \ref{['tab:simulations']} (dotted) and the simulations for $c_{\rm s}^2 \in \{10^{-7}, 10^{-5}\}$ (solid lines). Different DE EOS are presented in different colors, and the rows present the comparison and respective relative residuals at the selected redshifts $z\in\{0.0, 0.3, 0.9, 2.0\}$.