Five-dimensional warped product space-time with time-dependent warp factor and cosmology of the four-dimensional universe

Abstract

In this paper, we have studied a 5-dimensional warped product space-time with a time-dependent warp factor. This warp factor plays an important role in localizing matter to the 4-dimensional hypersurface constituting the observed universe and leads to a geometric interpretation of dynamical dark energy. The five-dimensional field equations are constructed and its solutions are obtained. The nature of modifications produced by this warp factor in the bulk geometry is discussed. The hypersurface is described by a flat FRW-type metric in the ordinary spatial dimension. It is found that the effective cosmological constant of the four-dimensional universe is a variable quantity monitored by the time-dependent warp factor. The universe is initially decelerated, but subsequently makes a transition to an accelerated phase at later times.

11 pages, no figures, accepted for publication in International Journal of Theoretical Physics

References in corpus (4)

• De Sitter brane-world, localization of gravity, and the cosmological constant
• Warped product spaces and geodesic motion in the neighbourhood of hypersurfaces
• Geodesic motion in the neighbourhood of submanifolds embedded in warped product spaces
• The warping of extra spaces accelerates the expansion of the universe