Cosmologies with a Dynamical Vacuum Energy

The possibility of a nonzero cosmological constant has been invoked several times in the past, both for theoretical and observational motivations. It has been often discarded by particle physicists, due to the huge difficulties in justifying a value of vacuum energy tiny enough to allow the universe to survive more than 10-41 s after the Big Bang. At present, the cosmological constant problem is still, probably, the most ununderstood issue of the physics. However, in recent times, it has again come into vogue, and again as a consequence of a number of observational evidences. Despite their apparent simplicity, the results of observations of more than 40 distant type lA supernovae seem to converge on the astonishing evidence that the present expansion of the universe is accelerating; this fact, together with many other experimental evidences of a lowdensity universe, and with the most recent CMB data indicating that the universe is very near to the flatness, has opened again the difficult question of what is the unobserved energy component that would balance a low-density universe with a flat one. At the same time, a new branch of cosmology has been opened, involving scalar fields as candidates for such "missing" energy. Motivated by the difficulties of cosmological constant models and by the most recent observational case of an accelerating universe, many alternative scenarios have been proposed: amongst them, the Quintessence scenarios, which are the subject of this thesis. In these models, the "missing energy" should reside in a dynamical scalar field rather than in a pure vacuum state; the dynamics of the field plays an important role, since the field energy density can adjust in a way that it comes to dominate at late times. The most important and distinctive feature of a scalar field vs. a cosmological constant, is that a field will develop fluctuations, that interact gravitationally with those of matter. To obtain the correct predictions of their impact on the Cosmic Microwave Background radiation and on the evolution of perturbations, the formalism of linear perturbation theory must be widely used. In this thesis we will focus on some basic issues connected with the attempt to build predictions on the cosmological impact of such scalar fields, following the results discussed in refs. [173, 174, 10, 15]. The first chapter is introductory and aims at giving an overview of the current observational evidences from which the case of a positive non-zero vacuum energy arises, motivating the consideration of the cosmological constant problem. In Chapter 2, the gauge-invariant formalism of linear cosmological perturbation theory is described, with particular attention to quantities such as the gravitational potentials, entropy and curvature perturbations, which are used in the following of the thesis. In Chapter 3 we recall some basic ideas on the mechanisms that generated the observed Cosmic Microwave Background of radiation, whose small but detectable anisotropies contain a large amount of information on the history of the Universe. In particular, CMB anisotropies turned out to be a very rich ground of investigation for discriminating between Quintessence and cosmological constant scenarios. These chapters set the framework for the results that will be presented in the following chapters, containing the original work of the thesis. In Chapter 4, focusing on scalar-type perturbations, we settled the analytical initial conditions that must be imposed on the components of cosmic fluid involving a minimally-coupled scalar field, in order to produce purely adiabatic or purely isocurvature initial conditions on super-horizon scales. Thus, an interesting comparison with the "standard" pure CDM flat model is performed. The distinctive imprints of Quintessence on large scale structure and on CMB anisotropies, both of polarization and temperature, are extensively analyzed. Chapter 5 extends the concept of Quintessence to a larger class of scalar fields, having an explicit coupling with the Ricci scalar in the Lagrangian. These more general models, here named "Extended Quintessence", are shown to enrich the phenomenology with respect to the simple minimally-coupled Quintessence. In fact, the predictions for the CMB anisotropies show new distinctive features, directly related to the presence of a non-zero coupling of the field with the gravitational sector of the Lagrangian and, ultimately, with the time-variation of the gravitational constant. A problem of "fine tuning" is however inherent both to cosmological constant and quintessence models: in order to have today an amount of vacuum energy comparable with that of matter, the vacuum energy density should have been initially vanishingly small. A way out to such fine tuning problem is possible in Quintessence scenarios, where one can select a subclass of models which admit "tracking solutions". This means that the present value of scalar field energy density, once fixed, can be determined starting from a very wide set of initial conditions, even though the tracking solutions are not perfect attractors and do not solve the problem of why the field energy density should have this value just today. Chapter 6 considers tracking behaviors in Extended Quintessence scenarios and presents a description of the rich phenomenology that arises from the corresponding dynamics; in particular, we show that the coupling with the Ricci scalar can act initially as an effective potential pushing the field in the tracking trajectory ( "R-boost"). The dependence of the phenomenology on the sign of the coupling constant is also described. Finally, Chapter 7 presents the conclusions and faces the future observational perspectives, on the light of the most recent data from MAXIMA and BOOMERANG-98 balloon experiments and of the future satellite missions MAP and Planck.