Particle Physics and Cosmology Confront the Cosmological Constant

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.