Cluster number counts dependence on dark energy inhomogeneities and coupling to dark matter

TL;DR

The paper investigates whether dark energy models that couple to dark matter and/or exhibit inhomogeneities on cluster scales leave observable imprints in galaxy cluster number counts. It develops a coupled quintessence framework with an exponential potential and a linear coupling to dark matter, and applies spherical collapse and the Press-Schechter formalism to quantify how coupling and inhomogeneity affect the mass function and redshift distribution. The authors find that stronger coupling reduces cluster counts via a decreasing comoving density and modified growth, while dark energy inhomogeneities increase counts, with oscillatory signatures in $\delta_c(z)$ and $\delta_L$ yielding distinctive wiggles in the counts. They show that future surveys like DES+SPT could detect these wiggles and discriminate between coupled quintessence and $\Lambda$CDM, highlighting the practical relevance of cluster statistics for probing dark sector physics.

Abstract

Cluster number counts can be used to test dark energy models. We investigate dark energy candidates which are coupled to dark matter. We analyze the cluster number counts dependence on the amount of dark matter coupled to dark energy. Further more, we study how dark energy inhomogeneities affect cluster abundances. It is shown that increasing the coupling reduces significantly the cluster number counts, and that dark energy inhomogeneities increases cluster abundances. Wiggles in cluster number counts are shown to be a specific signature of coupled dark energy models. Future observations will possibly detect such oscillations and discriminate among the different dark energy models.

Figures (6)

• Figure 1: Evolution of $\delta_c$ with redshift. Model A: $\Gamma_{\phi}\neq 0$, $\Omega_{\rm cDM}=0.25$, $\Omega_{\rm um}=\Omega_{b}=0.05$. Model B: $\Gamma_{\phi}\neq0$, $\Omega_{\rm cDM}=0.05$, $\Omega_{\rm um}+\Omega_{b}=0.25$. Model C: $\Gamma_{\phi}=0$, $\Omega_{\rm cDM}=0.25$, $\Omega_{\rm um}=\Omega_{b}=0.05$. Model D: $\Gamma_{\phi}=0$, $\Omega_{\rm cDM}=0.05$, $\Omega_{\rm um}+\Omega_{b}=0.25$. The $\Lambda CDM$ case, solid-line, is also plotted for reference.
• Figure 2: Evolution of the ratio $\delta_c / \sigma_8 D$ with redshift. Model A: $\Gamma_{\phi}\neq 0$, $\Omega_{\rm cDM}=0.25$, $\Omega_{\rm um}=\Omega_{b}=0.05$. Model B: $\Gamma_{\phi}\neq0$, $\Omega_{\rm cDM}=0.05$, $\Omega_{\rm um}+\Omega_{b}=0.25$. Model C: $\Gamma_{\phi}=0$, $\Omega_{\rm cDM}=0.25$, $\Omega_{\rm um}=\Omega_{b}=0.05$. Model D: $\Gamma_{\phi}=0$, $\Omega_{\rm cDM}=0.05$, $\Omega_{\rm um}+\Omega_{b}=0.25$. The $\Lambda CDM$ case is also plotted for reference.
• Figure 3: Comoving background matter density as a function of redshift. There is a decrease of density because of the coupling between dark matter and dark energy. Increasing the coupling leads to a faster decreasing of the comoving density with redshift. Wiggles are a characteristic signature of coupled quintessence models. Notice that in this plot non-coupled dark energy models would correspond to a constant line equal to one.
• Figure 4: Comoving volume compared to Einstein-de Sitter volume for the four study-models. Since the dark energy clustering does not affect the background evolution the difference is due only to the coupling. Models A and C with all dark matter coupled to dark energy have much more volume than models B and D, in which only a small fraction of dark matter is coupled. The concordance $\Lambda CDM$ model is also plotted for comparison.
• Figure 5: Redshift dependence of the number of clusters of $M > 2. \, 10^{14} M_{\odot} h^{-1}$ for square degree. All models are normalized to have the same number density of halos today. $\Lambda CDM$ case is also plotted for reference. Note the wiggles which are a feature of coupled dark energy models.