De Sitter thin brane model

Masato Nishi

doi:10.1093/ptep/ptw092

Abstract

We discuss the large mass hierarchy problem in a braneworld model which represents our acceleratively expanding universe. The Randall-Sundrum (RS) model with warped one extra dimension added to flat 4-dimensional space-time cannot describe our expanding universe. Here, we study instead the de Sitter thin brane model. This is described by the same action as that for the RS model, but the 4-dimensional space-time on the branes is $\rm dS_4$. We study the model for both the cases of positive 5-dimensional cosmological constant $\Lambda_5$ and negative one. In the positive $\Lambda_5$ case, the 4-dimensional large hierarchy necessitates a 5-dimensional large hierarchy, and we cannot get a natural explanation. On the other hand, in the negative $\Lambda_5$ case, the large hierarchy is naturally realized in the 5-dimensional theory in the same manner as in the RS model. Moreover, another large hierarchy between the Hubble parameter and the Planck scale is realized by the ${\mathcal O}(10^2)$ hierarchy of the 5-dimensional quantities. Finally, we find that the lightest mass of the massive Kaluza-Klein modes and the intervals of the mass spectrum are of order $10^2\,\rm GeV$, which are the same as in the RS case and do not depend on the value of the Hubble parameter.

Highlights

In the last 15 years, it has been believed that braneworld models may give a solution to the problem of the extremely large hierarchy between the Planck scale, 1019 GeV, and the weak scale, 102 GeV
Mpl(4+d) should be of order 1 TeV. This means that a too large Mpl is specific to the 4-dimensional theory, and the large hierarchy does not exist in higher dimensions
If we compactify the extra dimension by S1/Z2 to the RS model, two branes are naturally introduced at the fixed points

Summary

Introduction

In the last 15 years, it has been believed that braneworld models may give a solution to the problem of the extremely large hierarchy between the Planck scale, 1019 GeV, and the weak scale, 102 GeV. In 1998, Arkani-Hamed, Dimopoulos and Dvali first tried resolving the hierarchy problem by using a braneworld model [1, 2] Their explanation is as the follows: First, they assume a flat (4 + d)-dimensional space-time, in which the extra d-dimensions are compactified by a common radius L. Two branes are naturally introduced at the fixed points, y = 0, L They assume the energy scales (the vacuum expectation values of the Higgs boson) on the two branes to be 1019 GeV (the Planck scale) and 102 GeV (the weak scale), respectively. In the later two papers [8, 9], the author assumes one warped and uncompactified extra dimension y with negative Λ5 He introduces only a single brane with dS4 space-time.

Motivation for our work

Outline of the results

Setup and the classical solution

Exponential hierarchy

Graviton modes

Hierarchy problem

Zero-mode

Massive modes

Tachyonic modes

Parameter ξ

RS limit

Possibility of making the Hubble parameter timedependent