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The imprint of the interaction between dark sectors in galaxy clusters

Jian-Hua He, Bin Wang, Elcio Abdalla, Diego Pavon

TL;DR

This work investigates how interactions between dark energy and dark matter shape structure formation using perturbation theory, the Layzer–Irvine formalism, a multi-fluid spherical collapse model, and the Press–Schechter approach to cluster counts. By introducing phenomenological couplings with constants $\xi_1$ and $\xi_2$, the authors show that DE does not fully cluster with DM inside collapsing regions, leading to energy non-conservation in the linear regime. They derive modified virial conditions and compute the linear threshold $\delta_c(z)$ under homogeneous and inhomogeneous DE, then translate these into predictions for halo abundances under three coupling prescriptions and two normalization schemes. The findings indicate that cluster counts can carry signatures of dark-sector interactions, with the DE–DM coupling generally leaving a larger imprint than DE inhomogeneities, though the normalization choice can suppress or enhance the observable effects. Overall, the paper highlights cluster-count statistics as a potential probe of dark-sector physics and calls for careful treatment of DE inhomogeneities and normalization in interpreting such signatures.

Abstract

Based on perturbation theory, we study the dynamics of how dark matter and dark energy in the collapsing system approach dynamical equilibrium while interacting. We find that the interaction between dark sectors cannot ensure the dark energy to fully cluster along with dark, leading to the energy non-conservation problem in the collapsing system We examine the cluster number counts dependence on the interaction between dark sectors. Furthermore, we analyze how dark energy inhomogeneities affect cluster abundances. It is shown that cluster number counts can provide specific signature of dark sectors interaction and dark energy inhomogeneities.

The imprint of the interaction between dark sectors in galaxy clusters

TL;DR

This work investigates how interactions between dark energy and dark matter shape structure formation using perturbation theory, the Layzer–Irvine formalism, a multi-fluid spherical collapse model, and the Press–Schechter approach to cluster counts. By introducing phenomenological couplings with constants and , the authors show that DE does not fully cluster with DM inside collapsing regions, leading to energy non-conservation in the linear regime. They derive modified virial conditions and compute the linear threshold under homogeneous and inhomogeneous DE, then translate these into predictions for halo abundances under three coupling prescriptions and two normalization schemes. The findings indicate that cluster counts can carry signatures of dark-sector interactions, with the DE–DM coupling generally leaving a larger imprint than DE inhomogeneities, though the normalization choice can suppress or enhance the observable effects. Overall, the paper highlights cluster-count statistics as a potential probe of dark-sector physics and calls for careful treatment of DE inhomogeneities and normalization in interpreting such signatures.

Abstract

Based on perturbation theory, we study the dynamics of how dark matter and dark energy in the collapsing system approach dynamical equilibrium while interacting. We find that the interaction between dark sectors cannot ensure the dark energy to fully cluster along with dark, leading to the energy non-conservation problem in the collapsing system We examine the cluster number counts dependence on the interaction between dark sectors. Furthermore, we analyze how dark energy inhomogeneities affect cluster abundances. It is shown that cluster number counts can provide specific signature of dark sectors interaction and dark energy inhomogeneities.

Paper Structure

This paper contains 10 sections, 46 equations, 6 figures.

Table of Contents

  1. introduction
  2. PERTURBATION THEORY WHEN DE INTERACTS WITH DM
  3. Derivation of the Layzer-Irvine equation
  4. spherical collapse model and the Press-Schechter formalism
  5. cluster number counts
  6. Interaction proportional to the energy density of DE ($\xi_1=0,\xi_2 \neq 0$)
  7. The interaction proportional to the energy density of DM ($\xi_1>0,\xi_2=0$)
  8. Interaction proportional to the total energy density of dark sectors ($\xi=\xi_1=\xi_2>0$)
  9. Normalization
  10. conclusions and discussions

Figures (6)

  • Figure 1: The numerical results for the coupling proportional to the energy density of DE when the EOS of DE $w>-1$ . The solid lines show the results calculated with homogeneous DE distribution and the dotted lines are for the inhomogeneous distribution of DE.
  • Figure 2: The numerical results for the coupling proportional to the energy density of DE when the EOS of DE $w<-1$ . The solid lines show the results calculated when DE is distributed homogeneously and the dotted lines are for inhomogeneous DE model.
  • Figure 3: The numerical results for the coupling proportional to the energy density of DM. The solid lines shows the results calculated with homogeneous DE distribution and the dotted lines are for inhomogeneous DE.
  • Figure 4: The numerical results for the coupling proportional to the energy density of total dark sectors. The solid lines shows the results calculated with homogeneous DE distribution and the dotted lines are for inhomogeneous DE.
  • Figure 5: The results for the coupling proportional to the energy density of DE by fixing the local abundance.
  • ...and 1 more figures