Large-scale stable interacting dark energy model: Cosmological perturbations and observational constraints

TL;DR

The paper tackles instabilities in interacting dark-energy models with constant $w$ by designing a coupling $Q=3\beta H \frac{\rho_{\rm{de}}\rho_{\rm{c}}}{\rho_{\rm{de}}+\rho_{\rm{c}}}$ that behaves as $Q\propto\rho_{\rm{de}}$ at early times and $Q\propto\rho_{\rm{c}}$ in the future. It demonstrates that this model is equivalent to a decomposed generalized Chaplygin gas (NGCG) with $\beta=-\alpha w$, and develops gauge-invariant perturbation equations including the perturbation of $H$. The analysis shows stability for $\beta>0$ ($w>-1$) and uses Planck, SN, BAO, and $H_0$ data to constrain the model, finding $\beta=0.1385$ with $68\%$ CL $0.081<\beta<0.259$, i.e., positive coupling is favored. The results indicate that the decomposed NGCG formulation is a viable, observationally supported framework for interacting dark energy with potential for further theoretical and phenomenological exploration.

Abstract

Dark energy might interact with cold dark matter in a direct, nongravitational way. However, the usual interacting dark energy models (with constant $w$) suffer from some catastrophic difficulties. For example, the $Q\proptoρ_{\rm c}$ model leads to an early-time large-scale instability, and the $Q\proptoρ_{\rm de}$ model gives rise to the future unphysical result for cold dark matter density (in the case of a positive coupling). In order to overcome these fatal flaws, we propose in this paper an interacting dark energy model (with constant $w$) in which the interaction term is carefully designed to realize that $Q\proptoρ_{\rm de}$ at the early times and $Q\proptoρ_{\rm c}$ in the future, simultaneously solving the early-time superhorizon instability and future unphysical $ρ_{\rm c}$ problems. The concrete form of the interaction term in this model is $Q=3βH \frac{ρ_{\rm{de}}ρ_{\rm{c}}}{ρ_{\rm{de}}+ρ_{\rm{c}}}$, where $β$ is the dimensionless coupling constant. We show that this model is actually equivalent to the decomposed new generalized Chaplygin gas (NGCG) model, with the relation $β=-αw$. We calculate the cosmological perturbations in this model in a gauge-invariant way and show that the cosmological perturbations are stable during the whole expansion history provided that $β>0$. Furthermore, we use the Planck data in conjunction with other astrophysical data to place stringent constraints on this model (with eight parameters), and we find that indeed $β>0$ is supported by the joint constraint at more than 1$σ$ level. The excellent theoretical features and the support from observations all indicate that the decomposed NGCG model deserves more attention and further investigation.

Figures (3)

• Figure 1: The evolutions of gauge invariant matter perturbations and metric perturbations for $k=0.01\,\rm{Mpc^{-1}}$, $k=0.1\,\rm{Mpc^{-1}}$ and $k=1.0\,\rm{Mpc^{-1}}$. Here, we choose $w=-0.98$ and $\beta=0.1$, and fix other cosmological parameters at the best-fit values from Planck.
• Figure 2: The one-dimensional marginalized distributions and two-dimensional marginalized 68% and 95% contours, for the parameters in our interacting dark energy model.
• Figure B1: The evolutions of gauge invariant matter perturbations and metric perturbations for $k=0.01\,\rm{Mpc^{-1}}$, $k=0.1\,\rm{Mpc^{-1}}$ and $k=1.0\,\rm{Mpc^{-1}}$ in the case with the energy-momentum transfer parallel to the four-velocity of DE. Here, all the values of the cosmological parameters are set as the same as those used in Fig. \ref{['perturbationevolve']}.