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Cosmological Evolution With Interaction Between Dark Energy And Dark Matter

Yu. L. Bolotin, A. Kostenko, O. A. Lemets, D. A. Yerokhin

TL;DR

This review analyzes how interactions in the dark sector, specifically DE–DM couplings, reshape cosmic evolution beyond the standard cosmological model. It surveys a wide range of frameworks—from linear and nonlinear couplings to holographic, fractal, and modified-gravity realizations—and emphasizes both background dynamics and structure formation. A central contribution is the compilation of analytic results for several nonlinear interactions, duality relations, and phase-space structures, plus explicit realizations in chameleon fields, $f(R)$, $f(T)$ gravity, and holographic setups. The findings demonstrate that DE–DM coupling can drive or modify late-time acceleration, alleviate the cosmic coincidence problem, and even produce transient acceleration, with significant implications for observations and model-building.

Abstract

In this review we consider in detail different theoretical topics associated with interaction in the dark sector. We study linear and nonlinear interactions which depend on the dark matter and dark energy densities. We consider a number of different models (including the holographic dark energy and dark energy in a fractal universe) with interacting dark energy (DE) and dark matter (DM), have done a thorough analysis of these models. The main task of this review was not only to give an idea about the modern set of different models of dark energy, but to show how much can be diverse dynamics of the universe in these models. We find that the dynamics of a Universe that contains interaction in the dark sector can differ significantly from the Standard Cosmological Model (SCM).

Cosmological Evolution With Interaction Between Dark Energy And Dark Matter

TL;DR

This review analyzes how interactions in the dark sector, specifically DE–DM couplings, reshape cosmic evolution beyond the standard cosmological model. It surveys a wide range of frameworks—from linear and nonlinear couplings to holographic, fractal, and modified-gravity realizations—and emphasizes both background dynamics and structure formation. A central contribution is the compilation of analytic results for several nonlinear interactions, duality relations, and phase-space structures, plus explicit realizations in chameleon fields, , gravity, and holographic setups. The findings demonstrate that DE–DM coupling can drive or modify late-time acceleration, alleviate the cosmic coincidence problem, and even produce transient acceleration, with significant implications for observations and model-building.

Abstract

In this review we consider in detail different theoretical topics associated with interaction in the dark sector. We study linear and nonlinear interactions which depend on the dark matter and dark energy densities. We consider a number of different models (including the holographic dark energy and dark energy in a fractal universe) with interacting dark energy (DE) and dark matter (DM), have done a thorough analysis of these models. The main task of this review was not only to give an idea about the modern set of different models of dark energy, but to show how much can be diverse dynamics of the universe in these models. We find that the dynamics of a Universe that contains interaction in the dark sector can differ significantly from the Standard Cosmological Model (SCM).

Paper Structure

This paper contains 64 sections, 554 equations, 32 figures, 3 tables.

Table of Contents

  1. INTRODUCTION
  2. PHYSICAL MECHANISM OF ENERGY EXCHANGE
  3. Phenomenology of Interacting Models
  4. Simple Linear Models
  5. Non-linear interaction in the dark sector
  6. Case $Q=3H\gamma \frac{\rho_{dm} \rho_{dx} }{\rho } ,\quad \left(m,n,s\right)=\left(1,1,-2\right)$
  7. Case $Q=3H\gamma \frac{\rho_{dm}^{2} }{\rho } ,\quad \left(m,n,s\right)=\left(1,2,-2\right)$
  8. Case $Q=3H\gamma \frac{\rho_{de}^{2} }{\rho } ,\quad \left(m,n,s\right)=\left(1,0,-2\right)$
  9. Cosmological models with a change of the direction of energy transfer
  10. Case $Q=q(\alpha\dot{\rho}_m+3\beta H\rho_m)$
  11. Case $Q=q(\alpha\dot{\rho}_{tot}+3\beta H\rho_{tot})$
  12. Case $Q=q(\alpha\dot{\rho}_\Lambda+3\beta H\rho_\Lambda)$
  13. Degeneration problem
  14. Duality invariance and dynamics of interacting components
  15. Peculiarities of dynamics of scalar fields coupled to dark matter
  16. ...and 49 more sections

Figures (32)

  • Figure 1: $\Omega_m,$$\Omega_\Lambda,$$q$ and $w_{\rm eff}$ as functions of the redshift $z$ at $\Omega_{m0}=0.2738$ and $\beta=-0.010$ in the case $Q=3\beta qH\rho_m$HaoWei_Q(q)1.
  • Figure 2: Same as on Fig. \ref{['q-fig2']}, but for the case of interaction of the form $Q=3\beta qH\rho_{tot}$ under the condition $\beta\geq 0$HaoWei_Q(q)1.
  • Figure 3: Same as on Fig. \ref{['q-fig2']}, but for the case of $Q=3\beta qH\rho_\Lambda$HaoWei_Q(q)1.
  • Figure 4: The global phase portrait for $\omega=-1.49$ and $\gamma=1$. These diagrams show the evolution of a dust dominated Universe and include curves which can be interpreted as both the inflationary phase and the late time acceleration.
  • Figure 5: The global phase portrait for $\omega =-1.49$ and $\gamma=0$. These diagrams show the evolution of a dark matter dominated universe and include curves which can be interpreted as the manifestations of the late time acceleration.
  • ...and 27 more figures