Holographic dark energy models in LTB inhomogeneous universe

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.