Anti-Gravitating Brane-World Solutions for a de Sitter Brane in Scalar-Tensor Gravity

TL;DR

This paper explores five-dimensional scalar-tensor gravity models with branes, revealing solutions with positive cosmological constants that feature anti-gravitating regimes and exponential warp factors, advancing understanding of brane-world cosmology.

Contribution

It introduces novel brane-world solutions with positive cosmological constants in scalar-tensor gravity, highlighting anti-gravitating regimes and different scalar coupling effects.

Findings

Solutions exhibit anti-gravitating regimes away from the brane.

Exponential warp factors are found in both linear and quadratic coupling cases.

Positive cosmological constant on the brane correlates with anti-gravitating bulk regions.

Abstract

In the context of a five-dimensional theory with a scalar field non-minimally-coupled to gravity, we look for solutions that describe novel black-string or maximally-symmetric solutions in the bulk. The brane line-element is found to describe a Schwarzschild-(Anti)-de Sitter spacetime, and, here, we choose to study solutions with a positive four-dimensional cosmological constant. We consider two different forms of the coupling function of the scalar field to the bulk scalar curvature, a linear and a quadratic one. In the linear case, we find solutions where the theory, close to our brane, mimics an ordinary gravitational theory with a minimally-coupled scalar field giving rise to an exponentially decreasing warp factor in the absence of a negative bulk cosmological constant. The solution is characterised by the presence of a normal gravity regime around our brane and an anti-gravitating regime away from it. In the quadratic case, there is no normal-gravity regime at all, however, scalar field and energy-momentum tensor components are well-defined and an exponentially decreasing warp factor emerges again. We demonstrate that, in the context of this theory, the emergence of a positive cosmological constant on our brane is always accompanied by an anti-gravitating regime in the five-dimensional bulk.