Hybrid Inflation: Multi-field Dynamics and Cosmological Constraints
  The dynamics of hybrid models is usually approximated by the evolution of a
scalar field slowly rolling along a nearly flat valley. Inflation ends with a
waterfall phase, due to a tachyonic instability. This final phase is usually
assumed to be nearly instantaneous. In this thesis, we go beyond these
approximations and analyze the exact 2-field dynamics of hybrid models. Several
effects are put in evidence: 1) the possible slow-roll violations along the
valley induce the non existence of inflation at small field values. Provided
super-planckian fields, the scalar spectrum of the original model is red, in
agreement with observations. 2) The initial field values are not fine-tuned
along the valley but also occupy a considerable part of the field space
exterior to it. They form a structure with fractal boundaries. Using bayesian
methods, their distribution in the whole parameter space is studied. Natural
bounds on the potential parameters are derived. 3) For the original model,
inflation is found to continue for more than 60 e-folds along waterfall
trajectories in some part of the parameter space. The scalar power spectrum of
adiabatic perturbations is modified and is generically red, possibly in
agreement with CMB observations. Topological defects are conveniently stretched
outside the observable Universe. 4) The analysis of the initial conditions is
extended to the case of a closed Universe, in which the initial singularity is
replaced by a classical bounce. In the third part of the thesis, we study how
the present CMB constraints on the cosmological parameters could be ameliorated
with the observation of the 21cm cosmic background, by future giant
radio-telescopes. Forecasts are determined for a characteristic Fast Fourier
Transform Telescope, by using both Fisher matrix and MCMC methods.
