A Brane World Perspective on the Cosmological Constant and the Hierarchy Problems

TL;DR

This paper explores a brane world model where the smallness of the cosmological constant and the hierarchy problem are interconnected, proposing a scenario with multiple branes and adjustable bulk properties that address fundamental cosmological issues.

Contribution

It extends static brane world models to include multiple positive tension branes with adjustable bulk cosmological constants, linking solutions to the hierarchy and cosmological constant problems.

Findings

Exponential suppression of the 4-D cosmological constant when branes are far apart.

A Randall-Sundrum-like solution addressing the hierarchy problem.

An inequality relating the hierarchy and cosmological constant explains their observed values.

Abstract

We elaborate on the recently proposed static brane world scenario, where the effective 4-D cosmological constant is exponentially small when parallel 3-branes are far apart. We extend this result to a compactified model with two positive tension branes. Besides an exponentially small effective 4-D cosmological constant, this model incorporates a Randall-Sundrum-like solution to the hierarchy problem. Furthermore, the exponential factors for the hierarchy problem and the cosmological constant problem obey an inequality that is satisfied in nature. This inequality implies that the cosmological constant problem can be explained if the hierarchy problem is understood. The basic idea generalizes to the multibrane world scenario. We discuss models with piecewise adjustable bulk cosmological constants (to be determined by the 5-dimensional Einstein equation), a key element of the scenario. We also discuss the global structure of this scenario and clarify the physical properties of the particle (Rindler) horizons that are present. Finally, we derive a 4-D effective theory in which all observers on all branes not separated by particle horizons measure the same Newton's constant and 4-D cosmological constant.