  This pedagogical review aims at presenting the fundamental aspects of the
theory of inflationary cosmological perturbations of quantum-mechanical origin.
The analogy with the well-known Schwinger effect is discussed in detail and a
systematic comparison of the two physical phenomena is carried out. In
particular, it is demonstrated that the two underlying formalisms differ only
up to an irrelevant canonical transformation. Hence, the basic physical
mechanisms at play are similar in both cases and can be reduced to the
quantization of a parametric oscillator leading to particle creation due to the
interaction with a classical source: pair production in vacuum is therefore
equivalent to the appearance of a growing mode for the cosmological
fluctuations. The only difference lies in the nature of the source: an electric
field in the case of the Schwinger effect and the gravitational field in the
case of inflationary perturbations. Although, in the laboratory, it is
notoriously difficult to produce an electric field such that pairs extracted
from the vacuum can be detected, the gravitational field in the early universe
can be strong enough to lead to observable effects that ultimately reveal
themselves as temperature fluctuations in the Cosmic Microwave Background.
Finally, the question of how quantum cosmological perturbations can be
considered as classical is discussed at the end of the article.
