Brane world perspective on the cosmological constant and the hierarchy problems

Abstract

We elaborate on the recently proposed static brane world scenario, where the effective 4D 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. In addition to an exponentially small effective 4D 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 equation͒, a key element of the scenario. We also discuss the global structure of this scenario and clarify the physical properties of the particle ͑Rindler͒ horizons that are present. Finally, we derive a 4D effective theory in which all observers on all branes not separated by particle horizons measure the same Newton's constant and 4D cosmological constant.

Cosmology and fermion confinement in a scalar-field-generated domain wall brane in five dimensions

“…The properties of horizons in the case of a thin brane with no scalar field have been discussed in [12,13], and curvature singularities in the presence of a scalar field were considered in [23,24]. We have demonstrated the strong result that such features are inevitable in the case of a brane supported by a scalar field.…”

“…The ensuing cosmological evolution of the brane-bulk system has been studied extensively in the literature ( [7,8], or [8,9] for discussions of cosmology induced by moving branes). Many modifications and extensions to the initial RS scheme have also been proposed: see, for example [8,9,10,11,12,13].…”

Particle horizon and warped phenomenology

“…Furthermore, this change, from a discrete to a continuous KK spectrum, happens irrespective of whether the extra dimension is compactified or not. It has to do with the presence of the particle horizon that invariably appears in any scenario of the type of Ref [4,5] that naturally incorporates an exponentially small 4-D cosmological constant. In some sense, the phenomenology of the continuous gravity KK spectrum in this scenario (compactified or not) is quite similar to that on the probe brane [3] in the presence of the Planck brane in the uncompactified model also proposed by Randall and Sundrum [2].…”

“…Besides the above fine-tuning σ 1 = −σ 0 , the RS model also requires a fine-tuning between the brane tension and the bulk cosmological constant. In Ref [4,5], the bulk cosmological constants are treated as integration constants which are determined by the 5-D Einstein equation. This is made possible with the introduction of 5-form field strengths and/or unimodular gravity.…”

MINKOWSKI BRANE IN ASYMPTOTIC dS5 SPACETIME WITHOUT FINE-TUNING

“…All matter and interactions except gravity are confined to the 3-brane. Since the RS model was proposed, many physicists [4]- [18] have been trying to apply it to such issues as the hierarchy problem [11], cosmological constant problem [4,8,9,11,13,14,17,18], localization of gravity [7], dynamics of the brane [5], and the realization of the AdS 5 spacetime in string theory.…”