De Sitter brane-world, localization of gravity, and the cosmological constant

Ishwaree P. Neupane

doi:10.1103/PhysRevD.83.086004

paper

De Sitter brane-world, localization of gravity, and the cosmological constant

arXiv:1011.6357 · doi:10.1103/PhysRevD.83.086004

Abstract

Cosmological models with a de Sitter 3-brane embedded in a five-dimensional de Sitter spacetime (dS5) give rise to a finite 4D Planck mass similar to that in Randall-Sundrum (RS) brane-world models in AdS5 spacetime. Yet there arise a few important differences as compared to the results with a flat 3-brane or 4D Minkowski spacetime. For example, the mass reduction formula (MRF) $M_{P l}^{2} = M_{5}^{3} ℓ_{A d S}$ as well as the relationship $M_{P l}^{2} = M_{P l (4 + n)}^{n + 2} L^{n}$ (with $L$ being the average size or the radius of the $n$ extra dimensions) expected in models of product-space (or Kaluza-Klein) compactifications get modified in cosmological backgrounds. In an expanding universe, a physically relevant MRF encodes information upon the four-dimensional Hubble expansion parameter, in addition to the length and mass parameters $L$ , $M_{P l}$ and $M_{P l (4 + n)}$ . If a bulk cosmological constant is present in the solution, then the reduction formula is further modified. With these new insights, we show that the localization of a massless 4D graviton as well as the mass hierarchy between $M_{P l}$ and $M_{P l (4 + n)}$ can be explained in cosmological brane-world models. A notable advantage of having a 5D de Sitter bulk is that in this case the zero-mass wavefunction is normalizable, which is not necessarily the case if the bulk spacetime is anti de Sitter. In spacetime dimensions $D \geq 7$ , however, the bulk cosmological constant $Λ_{b}$ can take either sign ( $Λ_{b} < 0$ , $= 0$ , or $> 0$ ). The D=6 case is rather inconclusive, in which case $Λ_{b}$ may be introduced together with 2-form gauge field (or flux).

10 pages, 5 figures

De Sitter brane-world, localization of gravity, and the cosmological constant

Abstract

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