  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.
