  We investigate the constraints of slow-roll inflation on the string
worldsheet. A general gravity-matter set-up is used in which the worldsheet
consists of an abstract CFT coupled to a 3+1 dimensional non-linear sigma
model. The empirical slow-roll parameters are expressed in terms of the beta
functions of operators in the matter/internal CFT and the beta function of the
dilaton. The result confirms that inflation is only sensitive to macroscopic
properties of the matter sector, and that in string theory inflation is a
non-perturbative (in g_s) phenomenon and one must go beyond tree-level string
theory.
