  The presence of a cosmological constant, Lambda, in an action with higher
powers of the curvature can produce rapidly oscillating metrics. We develop a
perturbative approach for generating periodic solutions to the non-linear field
equations for such actions based on a small amplitude expansion. We find that
these oscillations have an amplitude proportional to \sqrt{\Lambda} and a
frequency of order the Planck mass. In a 4+1 dimensional scenario, a family of
metrics exists that are periodic in the extra dimension and are parameterized
by an effective four-dimensional cosmological constant which drives a rapid
oscillation.
