  In this thesis we investigate certain cosmological brane world models of the
Randall-Sundrum type. The models are motivated by string theory but we focus on
the phenomenology of the cosmology. Two models of specific interest are the
Dvali-Gabadadze-Porrati (DGP, induced-gravity) model, where the brane action is
modified, and the Gauss-Bonnet model where the bulk action is modified. Both of
these modifications maybe motivated by string theory. We provide a brief review
of Randall-Sundrum models and then consider the Kaluza-Klein modes on Minkowski
and de Sitter branes, in both the two and one brane cases. The spectrum
obtained for the de Sitter branes is a new result. We then consider a
Friedmann-Robertson-Walker brane in order to investigate the cosmological
dynamics on the brane. We present a brief discussion of the DGP and
Gauss-Bonnet brane worlds. We then investigate the Gauss-Bonnet-Induced-Gravity
(GBIG) model where the Gauss-Bonnet (GB) bulk term is combined with the
induced-gravity (IG) brane term of the DGP model. We present a thorough
investigation of cosmological dynamics, in particular focusing on GBIG models
that behave like self-accelerating DGP models at late times but at early times
show the remarkable feature of a finite-temperature Big Bang. We also discuss
the constraints from observations, including ages and Big Bang nucleosynthesis.
