Graviton localization and Newton law for a dS_4 brane in 5D bulk

TL;DR

This paper investigates how gravity behaves on a four-dimensional de Sitter brane within a five-dimensional bulk, analyzing graviton localization and the conditions under which Newton's law holds.

Contribution

It derives the graviton spectrum for a dS_4 brane in 5D bulk with various cosmological constants and identifies conditions for the validity of Newton's law.

Findings

Normalizable zero-mode exists for graviton localization.

Newton law is valid only with negative bulk cosmological constant.

Massive graviton states contribute at short distances.

Abstract

We consider an dS_4 brane embedded in a five-dimensional bulk with a positive, vanishing or negative bulk cosmological constant and derive the localized graviton spectrum that consists of a normalizable zero-mode separated by a gap from a continuum of massive states. We estimate the massive sector contribution to the static potential at short distances and find that only in the case of a negative bulk cosmological constant there is a range, determined by the effective four-dimensional and the bulk cosmological constants, where the conventional Newton law is valid.