  We investigate the cosmological consequences of a brane-world theory which
incorporates time variations in the gravitational coupling G and the
cosmological term Lambda. We analyze in detail the model where (dG/dt)/G ~ H
and Lambda ~ H^2, which seems to be favored by observations. We show that these
conditions single out models with flat space sections. We determine the
behavior of the expansion scale factor, as well as, the variation of G, Lambda
and H for different possible scenarios where the bulk cosmological constant can
be zero, positive or negative. We demonstrate that the universe must
recollapse, if it is embedded in an Anti-de Sitter five-dimensional bulk, which
is the usual case in brane models. We evaluate the cosmological parameters,
using some observational data, and show that we are nowhere near the time of
recollapse. We conclude that the models with zero and negative bulk
cosmological constant agree with the observed accelerating universe, while
fitting simultaneously the observational data for the density and deceleration
parameters. The age of the universe, even in the recollapsing case, is much
larger than in the FRW universe.
