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This thesis is centered on three main subjects within the theory of inflationand cosmological perturbations: loop corrections to the power spectrum ofcurvature fluctuations generated during inflation; evolution of cosmologicalfluctuations in anisotropic pre-inflationary cosmologies; statisticalanisotropy and non-Gaussianity predictions of models of inflation populatedwith vector fields. Currently, what makes even more interesting the study of2-nd and higher order corrections to cosmological correlation functions as wellas the computation of higher-than-two order correlators, is the almostunprecedented chance to confront theories with new and increasingly accurateexperimental data that will shed more light in the physics of the earlyUniverse. In the context of loop calculations, we have computed the correctionsarising from scalar-tensor interactions in models of single-field inflation(both for the standard slow-roll model and for models described by Lagrangianswith non-canonical kinetic terms). In the context of anisotropic cosmologies,also motivated by the observation of "anomalies" in the Cosmic MicrowaveBackground (CMB) fluctuations, we have computed the bispectrum and thetrispectrum of the curvature fluctuations in inflationary models with SU(2)vector fields, analyzing the statistical anisotropy features of the correlatorsin these models; finally, we have studied cosmological perturbations for aUniverse with a Bianchi type-I background metric, with an energy densitydominated by a pressureless fluid and in the presence of a cosmologicalconstant.

Cosmological correlation functions in scalar and vector inflationary models