Spacetime Symmetry and LemaîTre Class Dark Energy Models

Abstract

We present the regular cosmological models of the Lemaître class with time-dependent and spatially inhomogeneous vacuum dark energy, which describe relaxation of the cosmological constant from its value powering inflation to the final non-zero value responsible for the present acceleration in the frame of one self-consistent theoretical scheme based on the algebraic classification of stress-energy tensors and spacetime symmetry directly related to their structure. Cosmological evolution starts with the nonsingular non-simultaneous de Sitter bang, followed by the Kasner-type anisotropic expansion, and goes towards the present de Sitter state. Spacetime symmetry provides a mechanism of reducing cosmological constant to a certain non-zero value involving the holographic principle which singles out the special class of the Lemaître dark energy models with the global structure of the de Sitter spacetime. For this class cosmological evolution is guided by quantum evaporation of the cosmological horizon whose dynamics entirely determines the final value of the cosmological constant. For the choice of the density profile modeling vacuum polarization in a spherical gravitational field and the GUT scale for the inflationary value of cosmological constant, its final value agrees with that given by observations. Anisotropy grows quickly at the postinflationary stage, then remains constant and decreases to A < 10 − 6 when the vacuum density starts to dominate.

Universes Inside a Black Hole with the de Sitter Interior

“…A cosmological model related to a regular white hole (segment RC, W H, U in Figure 2, right) belongs to the cosmological models of the Lemaitre class with the de Sitter origin (for a review [21]). The regular white hole (more precisely its RC region) models the initial stages of a regular cosmology with the initial inflationary stage [26].…”

“…Stress-energy tensors specified by (1) generate spacetimes with the de Sitter center [18], and represent a spatially inhomogeneous and time evolving vacuum dark energy related to spacetime symmetry (for a review, see [19]). In the spacetime with a nonzero cosmological constant, λ, they relate two de Sitter vacua and describe relaxation of a cosmological constant from the big value, needed for driving inflation, to a small finite value [20] (for a review [21]). Regular solutions to the Einstein equations belong to the Kerr-Schild class and describe regular cosmological models and compact objects generically related to dark energy via their de Sitter interiors-regular black holes, their remnants, and self-gravitating vacuum solitons which can be responsible for observational effects related to a dark matter (for a recent review, see [22]).…”

Dark Matter Candidates with Dark Energy Interiors Determined by Energy Conditions

“…Introduced in this way vacuum dark fluid [13] can be both evolving and clustering. Solutions to the Einstein equations present, dependently on coordinate mapping, regular cosmological models with variable λ(ρ vac ) including initial, final and intermediate (if necessary) de Sitter stages [14][15][16] (for a review, see Reference [17]), and regular black holes (RBHs) and self-gravitating solitons G-lumps (particlelike structures without horizons replacing naked singularities) with the de Sitter interiors [13,18] (for a review, see Reference [19]). Mass M of an object is related to spacetime symmetry breaking from the de Sitter group at the origin [2].…”

Mass, Spacetime Symmetry, de Sitter Vacuum, and the Higgs Mechanism

“…1 Description of both these stages in the Universe evolution in the frame of a single self-consistent theoretical scheme is possible by introducing a cosmological term with the reduced symmetry, p r = −ρ (T t t = T r r ) which represents the time-dependent and spatially inhomogeneous vacuum dark energy. Relaxation of the cosmological constant from the initial big value to the presently observed value can be described in general setting by the spherically symmetric cosmology of the Lemaître class ( [76,77] and references therein). This picture is confirmed by two observational cases.…”