Revisit of the Interaction between Holographic Dark Energy and Dark Matter

TL;DR

This work revisits direct non-gravitational interactions between holographic dark energy and dark matter in a non-flat universe, testing three IHDE scenarios: two simple forms $Q\propto\rho_{dm}$ and $Q\propto\rho_{de}$ (IHDE1, IHDE2) and a general form $Q\propto\rho_{dm}^\alpha\rho_{de}^\beta$ (IHDE3). Using Union2.1+BAO+CMB+$H_0$ data in a joint $\chi^2$ analysis with MCMC, the authors find $c<1$ at 95.4% CL across all models and a slight preference for DM-to-DE energy flow ($\Gamma\lesssim 0$) at 68.3% CL, while the interaction generally has a small effect on the evolution of dark densities. The evolution and fate of the universe depend on the model: IHDE1 and IHDE2 typically lead to a big rip even with $c<1$, whereas IHDE3 can realize a de Sitter attractor in the future for large $\beta$, potentially avoiding the big rip. The study highlights degeneracies in the interaction parameters, the limited current sensitivity to the exact form of the interaction, and shows that a de Sitter future is achievable only in the generalized IHDE3 case under strong coupling.

Abstract

In this paper we investigate the possible direct, non-gravitational interaction between holographic dark energy (HDE) and dark matter. Firstly, we start with two simple models with the interaction terms $Q \propto ρ_{dm}$ and $Q \propto ρ_{de}$, and then we move on to the general form $Q \propto ρ_m^αρ_{de}^β$. The cosmological constraints of the models are obtained from the joint analysis of the present Union2.1+BAO+CMB+$H_0$ data. We find that the data slightly favor an energy flow from dark matter to dark energy, although the original HDE model still lies in the 95.4% confidence level (CL) region. For all models we find $c<1$ at the 95.4% CL. We show that compared with the cosmic expansion, the effect of interaction on the evolution of $ρ_{dm}$ and $ρ_{de}$ is smaller, and the relative increment (decrement) amount of the energy in the dark matter component is constrained to be less than 9% (15%) at the 95.4% CL. By introducing the interaction, we find that even when $c<1$ the big rip still can be avoided due to the existence of a de Sitter solution at $z\rightarrow-1$. We show that this solution can not be accomplished in the two simple models, while for the general model such a solution can be achieved with a large $β$, and the big rip may be avoided at the 95.4% CL.

Figures (9)

• Figure 1: Marginalized probability contours at the $68.3\%$ ($\Delta \chi^2 = 2.3$) and $95.4\%$ ($\Delta \chi^2 = 6.18$) CLs in the $\Gamma$--$c$ (for the three IHDE models) and $\Omega_{dm0}$--$c$ (for the HDE model) planes. The contours for the IHDE1 (cygan, labeled as I), IHDE2 (orange, labeled as II), and IHDE3 (olive, labeled as III) models are plotted in the left panel, and the contours for the HDE model (magnetic) are plotted in the right panel. The green dashed line denotes $c=1$. Clearly, compared with the HDE model, the fitting results of $c$ in the three IHDE models are smaller.
• Figure 2: Marginalized probability contours at the $68.3\%$ and $95.4\%$ CLs in the $\Gamma$--$\Omega_{k0}$ (left panel) and $\Omega_{dm0}$--$\Omega_{k0}$ (right panel) planes for the IHDE1 (cygan, labeled as I), IHDE2 (orange, labeled as II), IHDE3 (olive, labeled as III), and the HDE (magnetic) models. The $\Omega_{dm0}$--$\Omega_{k0}$ contours of the three IHDE models are similar to each other, so for the IHDE2 and IHDE3 models, we only plot the 95.4% CL contours.
• Figure 3: Marginalized probability contours at the $68.3\%$ and $95.4\%$ CLs in the $\alpha$--$\beta$ planes for the IHDE3 model.
• Figure 4: Reconstructed evolutions of $3H\rho_{dm}$, $3H(1+w_{eff})\rho_{de}$ and $Q$ (all divided by $\rho_{c0}$) at the 95.4% CL, for the IHDE1 (left panel), IHDE2 (middle panel) and IHDE3 (right panel) models, respectively.
• Figure 5: Evolutions of $E$, $\Omega_{de}$, $\Omega_{dm}$, $\Omega_{I}$, $w_{eff,de}$ and $w_{eff,dm}$ along with the scale factor $a$. Here we take typical values of $\Omega_{dm0}=0.24$, $\Omega_{k0}=0$, $h=0.73$, and others are denoted in the panel.