De Sitter brane-world, localization of gravity, and the cosmological
  constant
  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)
$M_{Pl}^2=M_{5}^3 \ell_{AdS}$ 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 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 $L$, $M_{Pl}$ 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 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 $D\ge 7$, however, the bulk cosmological constant
$\Lambda_b$ can take either sign ($\Lambda_b <0$, $=0$, or $>0$). The D=6 case
is rather inconclusive, in which case $\Lambda_b$ may be introduced together
with 2-form gauge field (or flux).
