De Sitter braneworld, localization of gravity, and the cosmological constant
Abstract
Cosmological models with a de Sitter 3brane embedded in a 5dimensional de Sitter spacetime (dS_{5}) give rise to a finite 4D Planck mass similar to that in RandallSundrum (RS) braneworld models in antide Sitter 5dimensional spacetime(AdS_{5}). Yet, there arise a few important differences as compared to the results with a flat 3brane or 4D Minkowski spacetime. For example, the mass reduction formula (MRF) M_{Pl}^{2}=M_{(5)}^{3}ℓ_{AdS} as well as the relationship M_{Pl}^{2}=M_{Pl(4+n)}^{n+2}L^{n} (with L being the average size or the radius of the n extra dimensions) expected in models of productspace (or KaluzaKlein) compactifications get modified in cosmological backgrounds. In an expanding universe, a physically relevant MRF encodes information upon the 4dimensional Hubble expansion parameter, in addition to the length and mass parameters L, M_{Pl}, and M_{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_{Pl} and M_{Pl(4+n)} can be explained in cosmological braneworld models. A notable advantage of having a 5D de Sitter bulk is that in this case the zeromass wave function is normalizable, which is not necessarily the case if the bulk spacetime is antide Sitter. In spacetime dimensions D≥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 2form gauge field (or flux). We obtain some interesting classical gravity solutions that compactify higherdimensional spacetime to produce a RobertsonWalker universe with de Sittertype expansion plus one extra noncompact direction. We also show that such models can admit both an effective 4dimensional Newton constant that remains finite and a normalizable zeromode graviton wave function.
 Publication:

Physical Review D
 Pub Date:
 April 2011
 DOI:
 10.1103/PhysRevD.83.086004
 arXiv:
 arXiv:1011.6357
 Bibcode:
 2011PhRvD..83h6004N
 Keywords:

 11.25.Mj;
 04.65.+e;
 11.25.Yb;
 98.80.Cq;
 Compactification and fourdimensional models;
 Supergravity;
 M theory;
 Particletheory and fieldtheory models of the early Universe;
 High Energy Physics  Theory;
 Astrophysics  Cosmology and Extragalactic Astrophysics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology
 EPrint:
 10 pages, 5 figures