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Stable Large-Scale Perturbations in Interacting Dark-Energy Model

Cheng-Yi Sun, Rui-Hong Yue

TL;DR

The paper addresses the instability of super-Hubble curvature perturbations in interacting dark energy models with constant $w_d$ and a simple coupling $Q\propto\rho_m$. It introduces a covariant energy-momentum transfer between dark energy and dark matter that conserves the total EMT in the dark sector and reduces to $Q=3\alpha H\rho_m$ at the background level. Through analysis of DE+CDM perturbations and then including radiation and baryons, the authors show the large-scale curvature perturbations remain stable and that dominant non-adiabatic modes grow only as a moderate power law (exponent of order unity). This supports the viability of covariant dark-sector interactions and provides a framework for stable perturbation evolution in cosmology.

Abstract

It is found that the evolutions of density perturbations on the super-Hubble scales are unstable in the model with dark-sector interaction $Q$ proportional to the energy density of cold dark matter (CDM) $ρ_m$ and constant equation of state parameter of dark energy $w_d$. In this paper, to avoid the instabilities, we suggest a new covariant model for the energy-momentum transfer between DE and CDM. Then we show that the the large-scale instabilities of curvature perturbations can be avoided in our model in the universe filled only by DE and CDM. Furthermore, by including the additional components of radiation and baryons, we calculate the dominant non-adiabatic modes in the radiation era and find that the modes grow in the power law with exponent at the order of unit.

Stable Large-Scale Perturbations in Interacting Dark-Energy Model

TL;DR

The paper addresses the instability of super-Hubble curvature perturbations in interacting dark energy models with constant and a simple coupling . It introduces a covariant energy-momentum transfer between dark energy and dark matter that conserves the total EMT in the dark sector and reduces to at the background level. Through analysis of DE+CDM perturbations and then including radiation and baryons, the authors show the large-scale curvature perturbations remain stable and that dominant non-adiabatic modes grow only as a moderate power law (exponent of order unity). This supports the viability of covariant dark-sector interactions and provides a framework for stable perturbation evolution in cosmology.

Abstract

It is found that the evolutions of density perturbations on the super-Hubble scales are unstable in the model with dark-sector interaction proportional to the energy density of cold dark matter (CDM) and constant equation of state parameter of dark energy . In this paper, to avoid the instabilities, we suggest a new covariant model for the energy-momentum transfer between DE and CDM. Then we show that the the large-scale instabilities of curvature perturbations can be avoided in our model in the universe filled only by DE and CDM. Furthermore, by including the additional components of radiation and baryons, we calculate the dominant non-adiabatic modes in the radiation era and find that the modes grow in the power law with exponent at the order of unit.

Paper Structure

This paper contains 8 sections, 45 equations, 2 figures.

Table of Contents

  1. Introduction
  2. New Covariant Model for Interaction in Dark Sector
  3. Evolution of Density Perturbations
  4. Evolving equations of Perturbations
  5. Adiabatic Initial Conditions
  6. Evolution of Curvature Perturbation on Large Scales
  7. Dominant Non-adiabatic Modes
  8. Conclusions and Discussions

Figures (2)

  • Figure 1: $\log_{10}{|\zeta|}$ versus $\log_{10}{a}$ in the interacting model for fixed $\Omega_{m0}=0.3$, $h=0.67$, $k=1.5\times10^{-4}\text{Mpc}^{-1}$, $\alpha=10^{-3}$ and different $w_d$.
  • Figure 2: $\log_{10}{|\zeta|}$ versus $\log_{10}{a}$ in the interacting model for fixed $\Omega_{m0}=0.3$, $h=0.67$, $k=1.5\times10^{-4}\text{Mpc}^{-1}$, $w_d=-0.94$ and different $\alpha$.