Perturbations in anisotropic cosmologies and cosmic no hair theorem

An introduction to the physics of inflation and to the no-hair theorem is presented, raising the unsolved question of whether or not inflation can occur in inhomogeneous cosmological models. A Bianchi type I (homogeneous and anisotropic) universe might degenerate into an inhomogeneous spacetime if small perturbations to the metric were introduced. This is verified with a perturbative analysis of density inhomogeneities and the results reveal that, for a large region of parameter space, the perturbations might reach order one well before what experimentally is indicated as the earliest time at which inflation might start. This provides a scenario in which it is not clear whether a De Sitter phase of the universe evolution will be eventually achieved.