Un ambiente geometrico per teorie perturbative in teorie di campo.

In this thesis we will introduce calculus of variations on composite bundles and its applications in the study of perturbation theory in field theories. Composite bundles can be thought as ladder of regular bundles. Hence, the category of composite bundles extends the category of bundles. As a consequence, the ordinary calculus of variations on bundles can be extended to this new category. We will use composite calculus of variations to get from a variational point of view the linearised equations associates to a given Lagrangian. This result can be achieved by considering an auxiliary Lagrangian on a specific composite bundle, whose composite variation will give the linearised equations together with field equations. At the end of this work we will also provide a physical example of these computations, in fact we are going to compute linearised Einstein equations starting from the Hilbert Lagrangian. Moreover, we will be able to check our results by fixing specific background metrics in order to get both the gravitational waves equations and the linearised Friedman equations.