Challenges for Superstring Cosmology

We consider whether current notions about superstring theory below the Planck scale are compatible with cosmology. We find that the anticipated form for the dilaton interaction creates a serious roadblock for inflation and makes it unlikely that the universe ever reaches a state with zero cosmological constant and time-independent gravitational constant. Superstring theories have been extensively studied as models of unified theories [1]. Effective field theories in four dimensions are used to describe string theory below the Planck scale. There are strong prejudices about the form that the four dimensional low energy effective field theory derived from superstrings must take in order for superstrings to be a viable model of particle interactions. In this paper, we extract the most generic elements of the “current superstring lore” (CSSL) and examine their implications for the early evolution of the universe. Our goal here is to be strict and systematic in bringing CSSL and cosmology together. Hence, it is necessary to carefully lay down the components of CSSL and to not deviate from them. In the past, several authors have encountered some of the cosmological problems of superstrings outlined below and have resorted to adding new terms in the effective potential to solve them [2]-[5]. However, these added terms violate one or more key tenets of present superstrings lore; the cosmology problems of CSSL are thereby masked. The main components of CSSL are: (1) The effective theory below the Planck scale is described by a weaklycoupled, four-dimensional, N = 1 supergravity field theory. Hence, the effective action is Kahler invariant, described by a real Kahler potential, K(φi), and a holomorphic superpotential W (φi):