On the four-dimensional effective theories in brane-worlds

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.