Localized gravity on de Sitter brane in five dimensions

TL;DR

This paper investigates gravity localization on a de Sitter brane in five-dimensional space, showing that four-dimensional gravity can be recovered via a zero mode, but the observed tiny cosmological constant cannot be explained in this model.

Contribution

It demonstrates the conditions for gravity localization on a de Sitter brane and relates the brane cosmological constant to fundamental scales, highlighting limitations in explaining the small observed cosmological constant.

Findings

Four-dimensional gravity is reproduced by a normalizable zero mode.

Massive modes are separated by a mass gap from the zero mode.

Tiny observed cosmological constant cannot be realized in this setup.

Abstract

We consider a single brane embedded in five dimensions with vanishing and positive bulk cosmological constant. In this setup, the existence of $dS_{4}$ brane is allowed. We explore the gravitational fluctuations on the brane, and we point out that the usual four-dimensional gravity can be reproduced by a normalizable zero mode and that the continuous massive modes are separated by a mass gap from zero mode. We derive the relation among the cosmological constant in the brane, and the fundamental scale of five dimensions and Planck scale. Finally we show that not zero but tiny observed cosmological constant cannot be realized in this setup.