The first two chapters are introductory and aim at giving a quick overview
of some work of the past and of the motivations for considering the cosmological
constant problem. These chapters are meant to be illustrative rather then
comprehensive. A more in depth historical introduction and a complete list of
references can be found in earlier reviews (33, 29, 116, 137, 163] on the subject. In
Chapter 1 we recall some basic ideas about the role of the cosmological constant
in particle physics and cosmology. The aim is to convince the reader that after
more than 70 years we still have some good reason to bother about the cosmological
constant. In Chapter 2, then, the idea of Quintessence is introduced and
recent results about cosmological rolling scalar fields are discussed. Here we set
the framework for the results that will be presented in the following chapters.
Finally, in Chapter 6, we present our conclusions.
