Accelerating Universes and String Theory

This article reviews recent developments in the study of universes with a positive cosmological constant in string theory. 1. The Challenge of Time It is evident that the world around us changes in time. At cosmological scales there is strong evidence that the universe was much hotter and denser some 13 billion years ago and has expanded and cooled since then, probably even undergoing an early period of exponentially accelerating expansion [1]. Apparently, even today a significant component of the matter in the universe is “dark energy” [1, 2], which might be a cosmological constant or a rolling scalar field [3] or something else, that is causing an accelerating expansion of spacetime. Despite these important motivations, very little is known about the basic features of string theory in expanding and time-dependent spacetimes, about the construction of realistic expanding universes from fundamental theory, about the nature of “dark energy” and the cosmological constant problem, and, most fundamentally, about “what time is”. More concretely, can the many light scalar fields (moduli) that arise in string compactifications acquire potentials that lead to slow roll inflation or quintessence, or perhaps can they be stabilized at a positive potential minimum giving a small cosmological constant? Expanding universes often begin in a big bang – can such spacelike curvature singularities including the ones inside Schwarzschild black holes be resolved in string theory? Is there a holographic description of universes with a positive cosmological constant akin to the ones available for a negative cosmological constant? Is information lost in black holes? It is important to mention that a fundamental challenge for string theory is that even the basic perturbative formulation of the theory is not understood in a general time-dependent spacetime. Recall that the sigma model approach to string perturbation theory constructs the partition function as a functional of the spacetime background