The holographic principle is investigated for the generalized Lemaitre–Tolman–Bondi (LTB) model of an inhomogeneous and an isotropic dark energy. The inhomogeneity is considered as spherically symmetric and locally flat overdense of dark energy with a few Gpc in size and has a core size on the scale of apparent horizon. Two particular forms of refined parabolic arbitrary scale function R(r, t) are used in the LTB metric and some cosmological functions are calculated and plotted with the cosmological time and the distance from the center of the inhomogeneity. By choosing specific values of some numerical parameters of the models, we showed that some of these functions are in agreement with recent observations and have behavior similar to that of the cosmological constant dark energy universe.

中文翻译：

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LTB非均匀宇宙中的全息暗能量模型

研究了非均匀和各向同性暗能量的广义勒梅特-托尔曼-邦迪 (LTB) 模型的全息原理。不均匀性被认为是球对称和局部平坦的暗能量密度过大，具有几个 Gpc 的大小，并且具有视视界尺度上的核心大小。LTB 度量中使用了两种特定形式的精制抛物线任意尺度函数 R(r, t)，并计算了一些宇宙学函数，并用宇宙学时间和距不均匀性中心的距离绘制了它们。通过选择模型的一些数值参数的特定值，我们表明其中一些函数与最近的观察一致，并且具有类似于宇宙常数暗能量宇宙的行为。