  Accelerating universe or the existence of a small and positive cosmological
constant is probably the most pressing obstacle as well as opportunity to
significantly improving the models of four-dimensional cosmology from
fundamental theories of gravity, including string theory. In seeking to resolve
this problem, one naturally wonders if the real world can somehow be
interpreted as an inflating de Sitter brane embedded in a higher-dimensional
spacetime described by warped geometry. In this scenario, the four-dimensional
cosmological constant may be uniquely determined in terms of two length scales:
one is a scale associated with the size of extra dimensions and the other is a
scale associated with the expansion rate of our universe. In some specific
cases, these two scales are complementary to each other. This result is
demonstrated here by presenting some explicit and completely non-singular de
Sitter space dS$_4$ solutions of vacuum Einstein equations in five and ten
dimensions.
