De Sitter and Minkowski Solutions in 4+1 Brane-World Models

TL;DR

This paper explores how certain 4+1 dimensional brane-world models can produce de Sitter and Minkowski solutions on a 3-brane, highlighting conditions for symmetry and the necessity of fine-tuning for Poincaré symmetry.

Contribution

It demonstrates that maximal 4D symmetry on the brane leads to a class of de Sitter solutions driven by brane tension and bulk scalar potential, with implications for the Cosmological Constant Problem.

Findings

De Sitter solutions are generated at a special dynamical point.

Small deviations from this point grow exponentially with e-folds.

Fine-tuning is required for Poincaré symmetry on the brane.

Abstract

We comment on approaches to the Cosmological Constant Problem in 4+1 dimensions, with the Standard Model fields confined to a 3-brane. We show that requiring maximal 4D symmetry only on this 3-brane (and not on all other 3-branes that foliate the 4+1-dimensional space) leads to a wide class of de Sitter solutions on the brane, with the Hubble constant sourced by the brane tension and a bulk scalar potential. For Poincar\'e symmetry on the brane, fine-tuning is always necessary. The de Sitter solutions are generated at a special dynamical point. Small deviations from this point are shown to grow exponentially with the number of e-folds.