Localized gravity on FRW branes

TL;DR

This paper investigates the conditions under which gravity can be localized on FRW branes within Schwarzschild anti de Sitter bulk, revealing that localization depends on the brane's cosmological constant and curvature, with implications for cosmological models.

Contribution

It provides a general proof of when gravity is localized on dynamic FRW branes, clarifying the role of cosmological constant and black hole mass in localization.

Findings

Gravity is not localized on AdS branes with AdS bulk.

Localization occurs only for specific curvature and cosmological constant conditions.

Negative cosmological constant on the brane is incompatible with gravity localization.

Abstract

We study the system of Schwarzschild anti de Sitter (S-AdS) bulk and FRW brane for localization of gravity; i.e. zero mass gravitons having ground state on the brane, and thereby recovering the Einstein gravity with high energy correction. It has been known that gravity is not localized on AdS brane with AdS bulk. We prove the general result that gravity is not localized for dynamic branes whenever Lambda_4 < 0, and is localized for the curvature index k = 1 only when Lambda_4 > 0 and black hole mass M not equal 0, else it is localized for all other FRW models. If the localization is taken as the brane world compatibility criterion for cosmological models, then it would predict that negative cosmological constant on the brane is not sustainable.