Covariant Analysis of Experimental Constraints on the Brane-world

TL;DR

This paper presents a covariant, model-independent analysis of observational constraints on brane-world theories, revealing that certain assumptions like reflection symmetry may be relaxed by considering higher dimensions, thus broadening the viable parameter space.

Contribution

It reformulates brane-world equations covariantly and demonstrates how higher dimensions can relax existing observational constraints, challenging previous assumptions.

Findings

Gravi-vectors and gravi-scalars are replaced by extrinsic curvature-related fields.

Reflection symmetry assumption in cosmological constraints is not necessary for brane-world models.

Higher dimensions can relax constraints from binary pulsar and inflation observations.

Abstract

Some observational constraints on the brane-world based on predictions from specific models in five dimensions, have been recently reported, both on local and cosmological scales. In order to identify the origins of these constraints, the equations of motion of the brane-world are translated to the most general, model-independent (or "covariant"), formulation of the theory, based only on the Einstein-Hilbert action for the bulk geometry, the confinement of the standard gauge interactions and the exclusive probing of the extra dimensions by the gravitational field. In the case of the binary pulsar PSR1913+16, it is found that gravi-vectors and gravi-scalars do not appear in the covariant equations, but they are replaced by vector and scalar fields related to the extrinsic curvature of the brane-world. Only the latter one impose a condition on the binary pulsar orbits. A general solution for this problem is proposed, based on results from differential geometry, suggesting a stable bulk geometry, whose existence requires higher dimensions. On the cosmological scale, it is shown that the high energy inflation constraint originating from the square of the energy density term in the modified Friedman's equation is mainly due to the assumption of the reflection symmetry across the brane-world. It is shown that this symmetry is not consistent with the regularity of the brane-world. These results suggest that the two constraints can be lifted by increasing the number of extra dimensions.