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Abstract

Assuming spherical symmetry we analyse the dynamics of an inhomogeneous dark radiation vaccum on a Randall and Sundrum 3-brane world. Under certain natural conditions we show that the effective Einstein equations on the brane form a closed system. On a de Sitter brane and for negative dark energy density we determine exact dynamical and inhomogeneous solutions which depend on the brane cosmological constant, on the dark radiation tidal charge and on its initial configuration. We also identify the conditions leading to the formation of a singularity or of regular bounces inside the dark radiation vaccum.

Torsion, Dirac Field, Dark Matter and Dark Radiation

“…This article has been prepared to study the role of torsion and the scalar field φ in gravitation, especially, in the presence of a Dirac field in the background of a particular class of RiemannCartan geometry of the space-time manifold and also try to study the possible connection of the field φ with dark matter [17,18] and dark radiation [19,20,21,22,23].…”

“…If we consider axial vector torsion together with a scalar field φ connected to a local scale factor [16], then the Euler-Lagrange equations not only give the constancy of the gravitational constant but they also link, in laboratory scale, the mass of the scalar field with the Nieh-Yan density and, in cosmic scale of FRW-cosmology, they predict only three kinds of the phenomenological energy density representing mass, radiation and cosmological constant. This article has been prepared to study the role of torsion and the scalar field φ in gravitation, especially, in the presence of a Dirac field in the background of a particular class of Riemann-Cartan geometry of the space-time manifold and also try to study the possible connection of the field φ with dark matter [17,18] and dark radiation [19,20,21,22,23].…”