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

Cosmological models with a de Sitter 3-brane embedded in a 5-dimensional de Sitter spacetime (dS5) 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(AdS5). 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) MPl2=M(5)3lAdS as well as the relationship MPl2=MPl(4+n)n+2Ln (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, MPl, and MPl(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 MPl and MPl(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 Λb can take either sign (Λb<0, =0, or >0). The D=6 case is rather inconclusive, in which case Λb 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.