  Models with extra dimensions have attracted much interest recently because
they may provide the solution for long standing problems in physics. One
interesting and very attractive idea is that our visible universe is confined
to a four-dimensional hypersurface in a higher-dimensional spacetime. This
membrane like universe was dubbed brane-world. The main goal of this thesis is
the study of the four-dimensional (4D) effective theories and their
observational consequences in the brane-world universe. After introducing the
brane-world idea with some detail we shall use the gradient expansion method to
obtain the 4D effective theories of gravity for several higher-dimensional
theories with different numbers of extra-dimensions. In the second half of the
thesis, after introducing the concept of brane-inflation we will focus on some
observational consequences of these low energy effective theories. In
particular, the last two chapters before the conclusion are devoted to the
study of non-Gaussianities in general models of inflation.
