Early Universe: inflation and cosmological perturbations

Talk given at the workshop "Geometry, Topology, QFT and Cosmology", Paris (28-30 May 2008); 23 pagesAfter a brief summary of general relativity and cosmology, we present the basic concepts underlying inflation, the currently best motivated models for the early Universe. We describe the simplest inflation models, based on a single scalar field, and discuss how primordial cosmological perturbations are generated. We then review some recent developments concerning multi-field inflation models, in particular multi-field Dirac-Born-Infeld inflation