De Sitter brane-world, localization of gravity, and the cosmological constant
- Department of Physics and Astronomy, University of Canterbury, Private Bag 4800, Christchurch 8041 (New Zealand)
Cosmological models with a de Sitter 3-brane embedded in a 5-dimensional de Sitter spacetime (dS{sub 5}) give rise to a finite 4D Planck mass similar to that in Randall-Sundrum (RS) brane-world models in anti-de Sitter 5-dimensional spacetime(AdS{sub 5}). 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{sub Pl}{sup 2}=M{sub (5)}{sup 3}l{sub AdS} as well as the relationship M{sub Pl}{sup 2}=M{sub Pl(4+n)}{sup n+2}L{sup 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 4-dimensional Hubble expansion parameter, in addition to the length and mass parameters L, M{sub Pl}, and M{sub Pl(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{sub Pl} and M{sub Pl(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 wave function is normalizable, which is not necessarily the case if the bulk spacetime is anti-de Sitter. In spacetime dimensions D{>=}7, however, the bulk cosmological constant {Lambda}{sub b} can take either sign ({Lambda}{sub b}<0, =0, or >0). The D=6 case is rather inconclusive, in which case {Lambda}{sub b} may be introduced together with 2-form gauge field (or flux). We obtain some interesting classical gravity solutions that compactify higher-dimensional spacetime to produce a Robertson-Walker universe with de Sitter-type expansion plus one extra noncompact direction. We also show that such models can admit both an effective 4-dimensional Newton constant that remains finite and a normalizable zero-mode graviton wave function.
- OSTI ID:
- 21541551
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 83, Issue 8; Other Information: DOI: 10.1103/PhysRevD.83.086004; (c) 2011 American Institute of Physics; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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COSMOLOGY AND ASTRONOMY
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BRANES
COMPACTIFICATION
COSMOLOGICAL CONSTANT
COSMOLOGICAL MODELS
DE SITTER SPACE
EXPANSION
GRAVITATION
KALUZA-KLEIN THEORY
MANY-DIMENSIONAL CALCULATIONS
MASS
MINKOWSKI SPACE
SPACE-TIME
UNIVERSE
WAVE FUNCTIONS
FIELD THEORIES
FUNCTIONS
MATHEMATICAL MODELS
MATHEMATICAL SPACE
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UNIFIED-FIELD THEORIES