Moduli Stabilization in String Gas Cosmology

Abstract

String gas cosmology is an approach towards studying the effects of superstring theory on early universe cosmology which is based on new symmetries and new degrees of freedom of string theory. Within this context, it appears possible to stabilize the moduli which describe the size and shape of the extra spatial dimensions without the need of introducing many extra tools such as warping and fluxes. In this lecture, the recent progress towards moduli stabilization in string gas cosmology is reviewed, and outstanding problems for the scenario are discussed. In this Introduction, the conceptual problems of scalar field-driven inflationary cosmology (our current paradigm of early universe cosmology) will be reviewed. These are some of the reasons which motivate the search for a new theory of the very early universe. It will then be explained why string theory offers the promise of successfully addressing some of these problems. However, any attempt to combine string theory with cosmology leads to new cosmological problems, most importantly the questions of why only three of the nine spatial dimensions of critical superstring theory are large, and why the moduli fields describing the volume and shape of the extra dimensions are stabilized. In the context of the current view of cosmology in which the temperature increases without bound as we venture into the past, it is clear that it is the ultimate theory which describes physics at the highest energies and on the smallest scales which will determine the evolution of the universe at the earliest times. At the moment, string theory is the best candidate of providing the required theory of matter at the highest energy scales. Thus, in the following we shall work under the hypothesis that string theory is indeed the correct theory of matter in the very early universe. However, there are also reasons coming from cosmology alone which might lead us to turn to string theory in the search for the theory of the very early universe: Most implementations of the inflationary universe scenario 1),2) (see also Refs. 3) and 4) for earlier ideas), the current paradigm of early universe cosmology, are based on the existence of a slowly rolling scalar field, the inflaton, whose energy-momentum tensor is dominated by the contribution of the field potential energy which drives a period of accelerated expansion. In spite of the impressive phenomenological successes of this paradigm in predicting the spectrum of density perturbations and the angular power spectrum of cosmic microwave background (CMB) anisotropies, the scalar field-driven inflationary universe scenario suffers from some important conceptual problems. 5),6) Addressing these problems is another of the goals of superstring