Vanishing of cosmological constant in nonfactorizable geometry

TL;DR

This paper extends Randall and Sundrum's model to include various four-dimensional backgrounds, demonstrating that a normalizable zero-mass graviton bound state exists only when the cosmological constant is zero, offering a dynamical explanation for its vanishing.

Contribution

It generalizes the Randall-Sundrum model to broader backgrounds and shows the zero-mass graviton state is normalizable only with zero cosmological constant.

Findings

Zero mass graviton bound state exists only if cosmological constant is zero.

Results applicable to Schwarzschild and de Sitter backgrounds.

Provides a dynamical reason for the vanishing of the cosmological constant.

Abstract

We generalize the results of Randall and Sundrum to a wider class of four-dimensional space-times including the four-dimensional Schwarzschild background and de Sitter universe. We solve the equation for graviton propagation in a general four dimensional background and find an explicit solution for a zero mass bound state of the graviton. We find that this zero mass bound state is normalizable only if the cosmological constant is strictly zero, thereby providing a dynamical reason for the vanishing of cosmological constant within the context of this model. We also show that the results of Randall and Sundrum can be generalized without any modification to the Schwarzschild background.