The property of dark energy, which is predicted as the physical reason for the accelerated expansion of the present universe and the coincidence problem by which are suppressed many dark energy models are two of the most difficult problems in modern cosmology. From the Wilkinson Microwave Anisotropy Probe (WMAP) the dark energy contributes about 73% of the total energy of the present universe. Also, the observations of type Ia supernovae (SNIa) suggest that the dark energy which have a huge negative pressure, yields to the transition of the universe from a deceleration to an acceleration phase at some redshift. We use the observation data for the SNIa, Cosmic Microwave Background (CMB) shift parameter, Baryonic Acoustic Oscillations (BAO) peak parameters and Hubble parameters to the transition of the universe and the consideration of the coincidence problem. In this work we reconstruct the interaction between HDE and DM, in which the coupling parameter is parameterized by the well-known Wetterich parameterization and is considered the evolution of the dark matter energy density. Our calculations show that the accurately calculated transition redshift is \(z_{t} = 0.89\) in the obtained model. We also calculate the present deceleration parameter \(q_{0}\) (−0.92) and resolve the coincidence problem.

暗能量的性质被预测为当前宇宙加速膨胀的物理原因，同时巧合问题也被抑制，许多暗能量模型被抑制，这是现代宇宙论中最困难的两个问题。来自威尔金森微波各向异性探测器（WMAP）的暗能量约占当前宇宙总能量的73％。同样，Ia型超新星（SNIa）的观测结果表明，具有巨大负压的暗能量会导致宇宙在某些红移下从减速阶段过渡到加速阶段。我们将观测数据用于SNIa，宇宙微波背景（CMB）偏移参数，重子声振荡（BAO）的峰值参数和哈勃参数向宇宙的过渡以及对重合问题的考虑。在这项工作中，我们重建了HDE和DM之间的相互作用，其中耦合参数通过众所周知的Wetterich参数化进行了参数化，并被认为是暗物质能量密度的演变。我们的计算表明，准确计算的过渡红移为在获得的模型中\（z_ {t} = 0.89 \）。我们还计算了当前的减速参数\（q_ {0} \）（−0.92）并解决了重合问题。