Parametric Amplification of Metric Fluctuations During Reheating in Two Field Models

It was recently suggested [1] that parametric resonance during the reheating phase of an inflationary Universe [2–4] may lead to an exponential amplification of superHubble scale gravitational fluctuations. If true, this would affect the usual predictions of inflationary models for observables such as the matter power spectrum and the spectrum of cosmic microwave anisotropies. In particular, it would require the coupling constants in the particle physics model of inflation to be exponentially smaller than previously thought in order that the theory does not generate a too large amplitude for the fluctuations. In Ref. [5] it was shown that, although there are no causality constraints which prohibit the amplification of super-Hubble (but sub-horizon) modes during reheating, the effect does not occur in a simple massive scalar field model of chaotic inflation based on the potential V (φ) = mφ/2 (Here, φ is the inflaton field). This is true even beyond the linear analysis [6]. Similarly, there is no effect for a quartic potential [7] V (φ) = λφ/4, nor for a potential containing both quadratic and quartic terms [8]. These results agree with the earlier analyses in Refs. [9] and [10]. It was then suggested [11] that the amplification of super-Hubble-scale modes would occur for two field models of inflation, e.g. for a model with potential