Adiabatic regularization in closed Robertson-Walker universes

Adiabatic regularization is a particularly efficient method of regularization for numerical studies of the dynamics of quantum scalar fields in homogeneous cosmological spacetimes. We show that of the possible ways to apply adiabatic regularization in a closed Robertson-Walker universe, only one yields the accepted trace anomaly and vacuum energy for a conformal scalar field. The method is to use the continuum measure appropriate to a flat space, while otherwise retaining the form of the subtractions appropriate to a closed space. We also show that this procedure is equivalent to point splitting, although technically much simpler.