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

TL;DR

This paper explores a five-dimensional warped space-time with a dynamic warp factor, explaining how it influences matter localization, dark energy, and the universe's transition from deceleration to acceleration.

Contribution

It introduces solutions for a 5D warped space-time with a time-dependent warp factor and analyzes its impact on 4D cosmology and dark energy.

Findings

Warp factor localizes matter to 4D hypersurface.

Effective cosmological constant varies over time.

Universe transitions from decelerated to accelerated expansion.

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.