  We renormalize the divergences in the energy-momentum tensor of a scalar
field that begins its evolution in an effective initial state. The effective
initial state is a formalism that encodes the signatures of new physics in the
structure of the quantum state of a field; in an inflationary setting, these
signatures could include trans-Planckian effects. We treat both the scalar
field and gravity equivalently, considering each as a small quantum fluctuation
about a spatially independent background. The classical gravitational equations
of motion then arise as a tadpole condition on the graviton. The contribution
of the scalar field to these equations contains divergences associated with the
structure of the effective state. However, these divergences occur only at the
initial time, where the state was defined, and they accompany terms depending
solely upon the classical gravitational background. We define the
renormalization prescription that adds the appropriate counterterms at the
initial-time boundary to cancel these divergences, and illustrate it with
several examples evaluated at one-loop order.
