General Properties of the Self-tuning Domain Wall Approach to the Cosmological Constant Problem

TL;DR

This paper investigates the self-tuning properties of brane world models with scalar fields, revealing that singularities are common and that fine-tuning is often necessary, but additional fields might restore self-tuning.

Contribution

It demonstrates the generic occurrence of singularities in self-tuning brane models and explores conditions for localized gravity and potential resolutions.

Findings

Singularities are common in self-tuned solutions with localized gravity.

Localized gravity with an infinite extra dimension requires fine-tuned brane tension.

Quantization of brane tension occurs in oscillatory potentials.

Abstract

We study the dynamics of brane worlds coupled to a scalar field and gravity, and find that self-tuning of the cosmological constant is generic in theories with at most two branes or a single brane with orbifold boundary conditions. We demonstrate that singularities are generic in the self-tuned solutions compatible with localized gravity on the brane: we show that localized gravity with an infinitely large extra dimension is only consistent with particular fine-tuned values of the brane tension. The number of allowed brane tension values is related to the number of negative stationary points of the scalar bulk potential and, in the case of an oscillatory potential, the brane tension for which gravity is localized without singularities is quantized. We also examine a resolution of the singularities, and find that fine-tuning is generically re-introduced at the singularities in order to retain a static solution. However, we speculate that the presence of additional fields may restore self-tuning.