The Cosmology of String Theoretic Axions
  String theory posesses numerous axion candidates. The recent realization that the compactification radius in string theory might be large means that these states can solve the strong CP problem. This still leaves the question of the cosmological bound on the axion mass. Here we explore two schemes for accommodating such light axions in cosmology. In the first, we note that in string theory the universe is likely to be dominated early on by the coherent oscillations of some moduli. The usual moduli problem assumes that these fields have masses comparable to the gravitino. We argue that string moduli are likely to be substantially more massive, eliminating this problem. In such cosmologies the axion bound is significantly weakened. Plausible mechanisms for generating the baryon number density are described. In the second, we point out that in string theory, the axion potentials might be much larger at early times than at present. In string theory, if CP violation is described by a small parameter, the axion may sit sufficiently close to its true minimum to invalidate the bounds. 
Tom Banks and Michael Dine