ABSTRACT
This chapter shows that it also contains some severe limitations requiring a very important extension: an initial stage of exponential expansion usually called the inflationary stage. There are three big problems within the Hot Big Bang model discussed so far: the flatness problem, the horizon problem and the origin of perturbations. A fourth problem is the so-called monopole problem. One could invoke the so-called anthropic principle to justify such a small deviation from flatness. The most evident way to show this point is based on cosmic microwave background observations. Until the end of seventies, there was no convincing solution to these problems. In 1981 Alan Guth showed that an initial phase of de Sitter expansion occurring before the radiation-dominated regime can actually explain both flatness and the homogeneity and isotropy of the universe without having to assume them as special initial conditions.
