  This paper investigates Starobinsky's model of inflation driven by the trace
anomaly of conformally coupled matter fields. This model does not suffer from
the problem of contrived initial conditions that occurs in most models of
inflation driven by a scalar field. The universe can be nucleated
semi-classically by a cosmological instanton that is much larger than the
Planck scale provided there are sufficiently many matter fields. There are two
cosmological instantons: the four sphere and a new ``double bubble'' solution.
This paper considers a universe nucleated by the four sphere. The AdS/CFT
correspondence is used to calculate the correlation function for scalar and
tensor metric perturbations during the ensuing de Sitter phase. The analytic
structure of the scalar and tensor propagators is discussed in detail.
Observational constraints on the model are discussed. Quantum loops of matter
fields are shown to strongly suppress short scale metric perturbations, which
implies that short distance modifications of gravity would probably not be
observable in the cosmic microwave background. This is probably true for any
model of inflation provided there are sufficiently many matter fields. This
point is illustrated by a comparison of anomaly driven inflation in four
dimensions and in a Randall-Sundrum brane-world model.
