Effectively four-dimensional spacetimes emerging from d=5 Einstein-Gauss-Bonnet Gravity

TL;DR

This paper explores how five-dimensional Einstein-Gauss-Bonnet gravity can dynamically reduce to effectively four-dimensional spacetimes, revealing unique solutions and symmetry breaking mechanisms relevant for connecting higher-dimensional theories to our observed universe.

Contribution

It uncovers a family of solutions showing dynamical dimensional reduction in five-dimensional Einstein-Gauss-Bonnet gravity when no constant-curvature vacuum exists.

Findings

Fifth dimension can compactify or shrink exponentially over time.

Symmetry breaking occurs near anti-de Sitter Chern-Simons theory.

Unique solutions within a certain class are identified.

Abstract

Einstein-Gauss-Bonnet gravity in five-dimensional spacetime provides an excellent example of a theory that, while including higher-order curvature corrections to General Relativity, still shares many of its features, such as second-order field equations for the metric. We focus on the largely unexplored case where the coupling constants of the theory are such that no constant-curvature solution is allowed, leaving open the question of what the vacuum state should then be. We find that even a slight deviation from the anti-de Sitter Chern-Simons theory, where the vacuum state is five-dimensional AdS spacetime, leads to a complete symmetry breakdown, with the fifth dimension either being compactified into a small circle or shrinking away exponentially with time. A complete family of solutions, including duality relations among them, is uncovered and shown to be unique within a certain class. This dynamical dimensional reduction scenario seems particularly attractive as a means for higher-dimensional theories to make contact with our four-dimensional world.