The Cosmological Constant and Warped Extra Dimensions

TL;DR

This paper explores a gravitational model with quadratic curvature terms and a scalar field in 4+1 dimensions, finding solutions that are compact and Poincare invariant without fine-tuning parameters like the cosmological constant.

Contribution

It demonstrates the existence of solutions in higher-dimensional gravity models that do not require fine-tuning of parameters, including the cosmological constant.

Findings

Solutions are compact in one dimension and Poincare invariant in others.

No fine-tuning needed for parameters, including the cosmological constant.

Universal inequalities constrain the parameters for solutions.

Abstract

We study the behavior of a general gravitational action, including quadratic terms in the curvature, supplemented by a compact scalar field in 4+1 dimensions. The generalized Einstein equation for this system admits solutions which are compact in one direction and Poincare invariant in the remaining directions. These solutions do not require any fine-tuning of the parameters in the action---including the cosmological constant---only that they should satisfy some mild inequalities. Some of these inequalities can be expressed in a universal form that does not depend on the number of extra compact dimensions when the scenario is generalized beyond 4+1 dimensions.