Cosmological inflation with orbifold moduli as inflatons

Cosmological inflation is studied in the case where the inflaton is the overall modulus T for an orbifold. General forms of the (non-perturbative) superpotential are considered to ensure that G=K+ln|W|2 is modular invariant. We find generically that these models do not produce a potential flat enough for slow roll to a supersymmetric minimum, although we do find a model which produces up to 20 e-folds of inflation to a non-supersymmetric minimum.