Lemaître dark energy model singled out by the holographic principle

We present a regular spherically symmetric cosmological model of the Lemaiˆ tre class which describes time-dependent and spatially inhomogeneous vacuum dark energy, has the same global structure as de Sitter space-time and is singled out by the holographic principle. The cosmological evolution is governed by quantum evaporation of the cosmological horizon and goes from a large initial value of the cosmological constant to a small final nonzero value which is tightly fixed by the quantum dynamics of the horizon. We study in detail the evolution of scale factors and the behavior of anisotropy during the whole evolution of the universe. For the choice of the density profile modeling vacuum polarization in a spherical gravitational field and the GUT scale initial value of the cosmological constant, its final value coincides with that given by observations. The anisotropy parameter grows quickly at the post-inflationary stage, then remains constant for a long time and decreases to the present epoch.