Probing interaction and spatial curvature in the holographic dark energy model

TL;DR

This work tests holographic dark energy (HDE) in a non-flat universe with possible interaction with matter by formulating three phenomenological Q terms. It derives the coupled evolution equations for the expansion history and the dark-energy density parameter under an IR cutoff tied to the future event horizon and solves them numerically for four model variants: HDE, KHDE, IHDE, and KIHDE. Using a joint analysis of SN Ia (Constitution sample), CMB shift parameter $R$, and BAO $A$, the study finds that both the interaction strength $b$ and the spatial curvature $\Omega_{k0}$ are individually small, but there is a strong degeneracy between them when both are allowed (KIHDE). Overall, the data favor a simple, non-interacting, flat HDE, yet the degeneracy highlights the importance of jointly marginalizing these parameters in cosmological fits and the potential for interaction and curvature to influence future constraints. The work clarifies how degeneracies between $b$ and $\Omega_{k0}$ manifest in holographic models and underscores the role of high-precision data in breaking them.

Abstract

In this paper we place observational constraints on the interaction and spatial curvature in the holographic dark energy model. We consider three kinds of phenomenological interactions between holographic dark energy and matter, i.e., the interaction term $Q$ is proportional to the energy densities of dark energy ($ρ_Λ$), matter ($ρ_{m}$), and matter plus dark energy ($ρ_m+ρ_Λ$). For probing the interaction and spatial curvature in the holographic dark energy model, we use the latest observational data including the type Ia supernovae (SNIa) Constitution data, the shift parameter of the cosmic microwave background (CMB) given by the five-year Wilkinson Microwave Anisotropy Probe (WMAP5) observations, and the baryon acoustic oscillation (BAO) measurement from the Sloan Digital Sky Survey (SDSS). Our results show that the interaction and spatial curvature in the holographic dark energy model are both rather small. Besides, it is interesting to find that there exists significant degeneracy between the phenomenological interaction and the spatial curvature in the holographic dark energy model.

Figures (5)

• Figure 1: Probability contours at $68.3\%$ and $95.4\%$ confidence levels in the $\Omega_{m0}-c$ plane, for the three IHDE models and the KHDE model.
• Figure 2: Probability contours at $68.3\%$ and $95.4\%$ confidence levels in the $\Omega_{m0}-b$ plane, for the three IHDE models.
• Figure 3: Probability contours at $68.3\%$ and $95.4\%$ confidence levels in the $c-b$ plane, for the three IHDE models.
• Figure 4: Probability contours at $68.3\%$ and $95.4\%$ confidence levels in the $\Omega_{m0}-\Omega_{k0}$ and $c-\Omega_{k0}$ planes, for the KHDE model.
• Figure 5: Probability contours at $68.3\%$ and $95.4\%$ confidence levels in the $\Omega_{k0}-b$ planes, for the three KIHDE models.