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The acceleration of the expansion of the Universe which has been identified in recent years has deep connections with some of the most central issues in fundamental physics. At present, the most plausible explanation is some form of vacuum energy. The puzzle of vacuum energy is a central question which lies at the interface between quantum theory and general relativity. Solving it will presumably require to construct a quantum theory of gravity and a correspondingly consistent picture of spacetime. To account for the acceleration of the expansion, one may also think of a more dynamical form of energy, what is known as dark energy, or modifications of gravity. In what follows, we review the the basic models for dark energy and the difficulties encountered in each approach, as well as we discuss the vacuum energy problem.

The cosmology of higher dimensional spacetimemodels in which ordinary matter is confined to ahypersurface (brane) is discussed. The nonconventionalaspects of the corresponding cosmological scenarios is emphasized. Some issues relevant to theprimordial universe, such as inflation, arereviewed.

This book describes the basic concepts of supersymmetric theories. It is aimed at theorists, experimentalists and cosmologists interested in supersymmetry, and its content is correspondingly divided into three distinct tracks of study. The topics covered include a discussion of the motivation for supersymmetry in fundamental physics, a description of the minimal supersymmetric model as well as models of grand unification and string models, a presentation of the main scenarios for supersymmetry breaking, including the concepts and results of dynamical breaking. On the astrophysics/cosmology side, the book includes discussions of supersymmetric dark matter candidates, inflation, dark energy, and the cosmological constant problem. Some very basic knowledge of quantum field theory is needed and extensive appendices (in particular an introduction to the Standard Model of fundamental interactions) allow the reader to refresh and complete their notions.

The mounting evidence that the universe is presently undergoing acceleratingexpansion has restored some credit to the scenarios with a nonvanishingcosmological constant. From the point of view of a theory of fundamentalinteractions, one may argue that a dynamical component with negative pressureis easier to achieve. As an illustration, the quintessence scenario is described andits shortcomings are discussed in connection with the nagging “cosmologicalconstant problem.”

Describing the presently observable Universe as a self-sustained condensate of gravitons of size \\(H_0^-1\\), with large occupation number \\(N\\), we argue that the most probable value for the quantum vacuum energy is of the order of the critical energy density, as observed.