The cosmological constant and warped extra dimensions - art. no. 084020

We study the behavior of a general gravitational action, including quadrati c terms in the curvature, supplemented by a compact scalar field in 4+1 dim ensions. 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 paramete rs 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 di mensions when the scenario is generalized beyond 4+1 dimensions.