Explosive particle production due to parametric resonance is a crucial feature of reheating in inflationary cosmology. Coherent oscillations of the inflaton field lead to a periodically varying mass in the evolution equation of matter and gravitational fluctuations and often induce a parametric resonance instability. In a previous paper [V. Zanchin et al., Phys. Rev. D $57,$ 4651 (1998)] it was shown that homogeneous (i.e. space-independent) noise leads to an increase of the generalized Floquet exponent for all modes, at least if the noise is temporally uncorrelated. Here we extend the results to the physically more realistic case of spatially inhomogeneous noise. We demonstrate—modulo some mathematical fine points which are addressed in a companion paper—that the Floquet exponent is a non-decreasing function of the amplitude of the noise. We provide numerical evidence for an even stronger statement, namely that in the presence of inhomogeneous noise, the Floquet exponent of each mode is larger than the maximal Floquet exponent of the system in the absence of noise.

• Received 4 January 1999

DOI:https://doi.org/10.1103/PhysRevD.60.023505