[Paper Review] Brane-World Multigravity

Antonios Papazoglou|ArXiv.org|Dec 11, 2001

Black Holes and Theoretical Physics1 references3 citations

TL;DR

This thesis proposes a brane-world multigravity scenario in which gravity at intermediate scales (1 mm to 10^26 cm) arises from ultralight massive gravitons in higher-dimensional spacetimes. By analyzing five- and six-dimensional models with flat or warped branes, the author demonstrates how negative tension branes generate Kaluza-Klein graviton modes, stabilizes moduli via bulk scalar dynamics, and realizes viable multigravity without the van Dam-Veltman-Zakharov discontinuity, culminating in a phenomenologically viable six-dimensional model with flat positive-tension branes.

ABSTRACT

In this thesis, we discuss the idea of multigravity, namely the possibility that a significant component of gravity that we feel at intermediate distances (1 mm < r < 10^26 cm) is due to massive but ultralight gravitons. We demonstrate how this phenomenon can be realized in brane-world models in a spacetime with more than four dimensions and discuss how modifications of gravity at cosmological scales emerge as a consequence. Firstly, we consider five dimensional multigravity models with flat branes. We see how the existence of freely moving negative tension branes gives rise to ultralight graviton Kaluza-Klein states. Secondly, we study the moduli corresponding to the position of the branes and the size of the extra dimension, the radions and the dilaton respectively. We show that the radions corresponding to negative tension branes have wrong sign kinetic term. We also derive a stabilization condition for the dilaton in a brane model with general bulk scalar field dynamics. Thirdly, we show how we can reproduce the five dimensional multigravity models with Anti-de Sitter branes of positive tension only. Moreover, we demonstrate how the van Dam-Veltman-Zakharov discontinuity can be circumvented at tree level in Anti-de Sitter space. Finally, we discuss how the above multigravity models can be replicated in six dimensions with flat positive tension branes. This last possibility is the first theoretically and phenomenologically viable realization of the multigravity scenario.

Motivation & Objective

• To explore the viability of multigravity scenarios where intermediate-scale gravity is mediated by ultralight massive gravitons in higher-dimensional spacetimes.
• To analyze the role of negative tension branes in generating Kaluza-Klein graviton modes in five-dimensional brane-world models.
• To derive and solve the stabilization condition for the dilaton and radion moduli in higher-dimensional gravity models with general bulk scalar dynamics.
• To demonstrate how the van Dam-Veltman-Zakharov discontinuity can be avoided at tree level in Anti-de Sitter space.
• To construct the first theoretically and phenomenologically viable multigravity model in six dimensions using flat positive-tension branes.

Proposed method

• Constructs five-dimensional brane-world models with flat or Anti-de Sitter bulk spacetimes and multiple three-branes, including negative tension branes.
• Derives the effective action for the graviton-radion-dilaton system using Kaluza-Klein mode decomposition and perturbative expansion around background metrics.
• Analyzes the kinetic terms of radion modes associated with negative tension branes, showing they carry a wrong-sign kinetic energy.
• Derives a general stabilization condition for the dilaton in warped backgrounds using equations of motion from a bulk scalar field Lagrangian.
• Applies sum rules and propagator analysis to study gravity propagation on branes and the behavior of massive graviton modes.
• Constructs a six-dimensional multigravity model with flat positive-tension branes, showing it reproduces the desired multigraviton spectrum without the vDVZ discontinuity.

Experimental results

Research questions

• RQ1 Can multigravity with ultralight massive gravitons be consistently realized in higher-dimensional brane-world models?
• RQ2 How do negative tension branes affect the spectrum and stability of Kaluza-Klein graviton modes in five-dimensional models?
• RQ3 What is the general condition for dilaton stabilization in warped backgrounds with arbitrary bulk scalar field dynamics?
• RQ4 Can the van Dam-Veltman-Zakharov discontinuity be avoided in Anti-de Sitter space at tree level in multigravity models?
• RQ5 Is there a six-dimensional brane-world model with flat positive-tension branes that realizes a viable and phenomenologically consistent multigravity scenario?

Key findings

• Negative tension branes in five-dimensional models lead to Kaluza-Klein graviton modes that are ultralight and contribute to intermediate-scale gravity.
• Radion modes associated with negative tension branes possess a wrong-sign kinetic term, indicating potential instability unless stabilized by other mechanisms.
• A general stabilization condition for the dilaton is derived in warped backgrounds, depending on the dynamics of the bulk scalar field.
• The van Dam-Veltman-Zakharov discontinuity is circumvented at tree level in Anti-de Sitter space due to the specific structure of the graviton propagator.
• A six-dimensional multigravity model with flat positive-tension branes is constructed that realizes the multigravity scenario without the vDVZ discontinuity and is the first theoretically and phenomenologically viable realization of the idea.
• The model exhibits quasi-localized gravity on the brane and supports a spectrum of massive gravitons consistent with intermediate-scale gravity phenomenology.