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On the growth of perturbations in interacting dark energy and dark matter fluids

N. A. Koshelev

TL;DR

The paper addresses perturbation growth in interacting dark energy–dark matter using covariant couplings, focusing on a product-density rate $\bar{Q} \sim \gamma \bar{\rho}_c^{\alpha} \bar{\rho}_x^{\beta}$. It derives the perturbation equations within a two-fluid covariant framework, analyzes large-scale stability, and examines a main $\alpha=\beta=1$ case as well as a velocity-dependent special case $Q^{\mu} = \gamma \rho_c\rho_x (u_c - u_x)$. The authors find that, in the radiation era, the model with $\gamma>0$ generally avoids large-scale instabilities for $w_x(a) > -1/3$, while $\gamma<0$ can induce rapid growth of non-adiabatic perturbations in certain regimes; a subset of parameter choices remains viable. These results guide viable parameter ranges for interacting dark sectors and have implications for early-universe cosmology and observational constraints.

Abstract

The covariant generalizations of the background dark sector coupling suggested in G. Mangano, G. Miele and V. Pettorino, Mod. Phys. Lett. A 18, 831 (2003) are considered. The evolution of perturbations is studied with detailed attention to interaction rate that is proportional to the product of dark matter and dark energy densities. It is shown that some classes of models with coupling of this type do not suffer from early time instabilities in strong coupling regime.

On the growth of perturbations in interacting dark energy and dark matter fluids

TL;DR

The paper addresses perturbation growth in interacting dark energy–dark matter using covariant couplings, focusing on a product-density rate . It derives the perturbation equations within a two-fluid covariant framework, analyzes large-scale stability, and examines a main case as well as a velocity-dependent special case . The authors find that, in the radiation era, the model with generally avoids large-scale instabilities for , while can induce rapid growth of non-adiabatic perturbations in certain regimes; a subset of parameter choices remains viable. These results guide viable parameter ranges for interacting dark sectors and have implications for early-universe cosmology and observational constraints.

Abstract

The covariant generalizations of the background dark sector coupling suggested in G. Mangano, G. Miele and V. Pettorino, Mod. Phys. Lett. A 18, 831 (2003) are considered. The evolution of perturbations is studied with detailed attention to interaction rate that is proportional to the product of dark matter and dark energy densities. It is shown that some classes of models with coupling of this type do not suffer from early time instabilities in strong coupling regime.

Paper Structure

This paper contains 6 sections, 54 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Background.
  3. Model and perturbed equations.
  4. Large scale perturbations.
  5. Special case.
  6. Conclusions.

Figures (2)

  • Figure 1: Background energy densities in units of $\rho_{0cr}$ for $\alpha=\beta=1$, $H_0=70$ km s${}^{-1}$Mpc${}^{-1}$, $\Omega_x=0.70$, $\Omega_c=0.2538$, $\Omega_b=0.0462$. Examples of dark sector densities evolution at negative and positive coupling are shown on left and right panels, respectively.
  • Figure 2: a) The curvature perturbation $\zeta$ on super-Hubble scale in models with coupling (\ref{['coupl_2']}) and constant dark energy equation of state $w_x<-1/3$. Growth of the non-adiabatic perturbations begins at the stage of the strong interaction. b)The density perturbation evolution in model with $w_x>-1/3$ in radiation dominated era. Initial dark sector conditions are set at $\tau_{in}=2\times 10^{-8}$ Mpc by $\delta\rho_c/\bar{\rho}_c'= \delta\rho_x/\bar{\rho}_x'= \delta\rho_r/\bar{\rho}_r'$, $\theta_x(\tau_{in})=0$. In both cases the background densities corresponds to present values $\Omega_x=0.70$, $\Omega_c=0.2538$, $\Omega_b=0.0462$, the initial curvature perturbation $\zeta(\tau_{in})$ equal to $1\times 10^{-25}$ and comoving wave number is $k = 7 \times 10^{-5}$ Mpc${}^{-1}$.