Fluctuations, Ghosts, and the Cosmological Constant

Abstract

For a large region of parameter space involving the cosmological constant and mass parameters, we discuss fluctuating spacetime solutions that are effectively Minkowskian on large time and distance scales. Rapid, small amplitude oscillations in the scale factor have a frequency determined by the size of a negative cosmological constant. A field with modes of negative energy is required. If it is gravity that induces a coupling between the ghost-like and normal fields, we find that this results in stochastic rather than unstable behavior. The negative energy modes may also permit the existence of Lorentz invariant fluctuating solutions of finite energy density. Finally we consider higher derivative gravity theories and find oscillating metric solutions in these theories without the addition of other fields.