Aspects of thick brane worlds: 4D gravity localization, smoothness, and mass gap

TL;DR

This paper reviews thick brane models in 5D gravity with scalar fields, exploring how different geometric and spectral properties affect 4D gravity localization, the presence of mass gaps, and the implications for singularities and model viability.

Contribution

It analyzes the conditions under which thick brane models exhibit smooth geometries, mass gaps, and physically acceptable boundary conditions, advancing understanding of 4D gravity localization in these scenarios.

Findings

Smooth geometries have a continuous spectrum with no mass gap.

Models with a mass gap feature a massive bound state and a naked singularity.

Imposing boundary conditions can eliminate singularities and ensure model viability.

Abstract

We review some interrelated aspects of thick brane worlds constructed within the framework of 5D gravity coupled to a scalar field depending on the extra dimension. It turns out that when analyzing localization of 4D gravity in this smooth version of the Randall-Sundrum model, a kind of dichotomy emerges. In the first case the geometry is completely smooth and the spectrum of metric fluctuations shows a single massless bound state, corresponding to the 4D graviton, and a tower of massive states described by a continuous spectrum of Kaluza-Klein excitations starting from zero mass, indicating the lack of a mass gap. In the second case, there are two bound states, a massless 4D graviton and a massive excitation, separated by a mass gap from a continuous spectrum of massive modes; nevertheless, the presence of a mass gap in the graviton spectrum of the theory is responsible for a naked singularity at the boundaries (or spatial infinity) of the Riemannian manifold. However, the imposition of unitary boundary conditions, which is equivalent to eliminating the continuous spectrum of gravitational massive modes, renders these singularities harmless from the physical point of view, providing the viability of the model.