Asymmetrically warped R=0 braneworlds

TL;DR

This paper introduces a new family of five-dimensional braneworld models with asymmetric warp factors, analyzing their geometric properties, energy conditions, and effective four-dimensional cosmological implications.

Contribution

It presents novel solutions for asymmetrically warped R=0 braneworlds, exploring their energy conditions and effective cosmological constants, extending previous symmetric models.

Findings

Energy conditions hold for a range of warp parameter values.

Energy density and pressures decay as inverse square of the extra dimension.

Projection yields an effective cosmological constant on the brane.

Abstract

A new family of five dimensional, R=0 braneworlds with asymmetric warp factors is proposed. Beginning with the invariance of the Ricci scalar for the general class of asymmetrically warped spacetimes we, subsequently specialise to the R=0 case. Solutions are obtained by choosing a particular relation (involving a parameter $\nu$) between the warp factors. Symmetric warping arises as a special case (particular value of $\nu$). Over a range of values of $\nu$ the energy conditions for the matter stress energy are found to hold good. It turns out that the energy density and pressures required to support these spacetimes decay as the inverse square of the fifth (extra) coordinate. The projection of this bulk stress--energy (for symmetric warping) on the 3--brane yields an effective cosmological constant. We conclude with brief comments on spacetimes with constant Ricci scalar and the extension of our results to diverse dimensions.