Parametric Resonance For Complex Fields

Recently, there have been studies of parametric resonance decay of oscillating real homogeneous cosmological scalar fields, in both the narrow-band and broad-band case, primarily within the context of inflaton decay and (p)reheating. However, many realistic models of particle cosmology, such as supersymmetric ones, inherently involve complex scalar fields. In the oscillations of complex scalars, a relative phase between the oscillations in the real and imaginary components may prevent the violations of adiabaticity that have been argued to underly broad-band parametric resonance. In this paper, we give a treatment of parametric resonance for the decay of homogeneous complex scalar fields, analyzing properties of the resonance in the presence of out of phase oscillations of the real and imaginary components. For phase-invariant coupling of the driving parameter field to the decay field, and Mathieu type resonance, we give an explicit mapping from the complex resonance case to an equivalent real case with shifted resonance parameters. In addition, we consider the consequences of the complex field case as they apply to ``instant preheating,'' the explosive decay of non-convex potentials, and resonance in an expanding FRW universe. Applications of our considerations to supersymmetric cosmological models will be presented elsewhere.