Lectures on inflation and cosmological perturbations
  The purpose of these lectures is to give a pedagogical introduction to
inflation and the production of primordial perturbations, as well as a review
of some of the latest developments in this domain. After a short introduction,
we review the main principles of the Hot Big Bang model, as well as its
limitations. This motivates the study of cosmological inflation induced by a
slow-rolling scalar field. We then turn to the analysis of cosmological
perturbations, and explain how the vacuum quantum fluctuations are amplified
during an inflationary phase. The next step consists in relating the
perturbations generated during inflation to the perturbations of the
cosmological fluid in the radiation dominated phase. The final part of these
lectures gives a review of more general models of inflation, involving multiple
fields or non standard kinetic terms. Although more complicated, these models
are usually motivated by high energy physics and they can lead to specific
signatures that are not expected in the simplest models of inflation. After
introducing a very general formalism to describe perturbations in multi-field
models with arbitrary kinetic terms, several interesting cases are presented.
We also stress the role of entropy perturbations in the context of multi-field
models. Finally, we discuss in detail the non-Gaussianities of the primordial
perturbations and some models that could produce a detectable level of
non-Gaussianities.
