We examine the renormalization of an effective theory description of a general initial state set in an isotropically expanding space-time, which is done to understand how to include the effects of new physics in the calculation of the cosmic microwave background power spectrum. The divergences that arise in a perturbative treatment of the theory are of two forms: those associated with the properties of a field propagating through the bulk of space-time, which are unaffected by the choice of the initial state, and those that result from summing over the short-distance structure of the initial state. We show that the former have the same renormalization and produce the same subsequent scale dependence as for the standard vacuum state, while the latter correspond to divergences that are localized at precisely the initial time hypersurface on which the state is defined. This class of divergences is therefore renormalized by adding initial-boundary counterterms, which render all of the perturbative corrections small and finite. Initial states that approach the standard vacuum at short distances require, at worst, relevant or marginal boundary counterterms. States that differ from the vacuum at distances below that at which any new, potentially trans-Planckian, physics becomes important are renormalized with irrelevant boundary counterterms.