Classical Decay of the Inflaton

Abstract

We present the first fully nonlinear calculation of inflaton decay. We map inflaton decay onto an equivalent classical problem and solve the latter numerically. In the lf 4 model, we find that parametric resonance develops slower and ends at smaller values of fluctuating fields, as compared to estimates existing in literature. We also observe a number of qualitatively new phenomena, including a stage of semiclassical thermalization, during which the decay of inflaton is essentially as effective as during the resonance stage. [S0031-9007 (96)00641-2] PACS numbers: 98.80.Cq, 05.70.FhAmplification of quantum fluctuations and transition to semiclassical behavior are familiar subjects in inflationary cosmology (for a review of the latter, see Ref.[1]). Semiclassical fluctuations produced during inflation can explain the observed large scale structure of the Universe [2]. The theory of their production is by now well developed; for a recent rather general presentation, see Ref.[3]. After inflation ends, the scalar field (inflaton) that was driving it begins to oscillate. These oscillations are thought to lead to particle production, inflaton decay, and eventually to reheating of the Universe.It was only recently realized that phenomena related to large occupation numbers of Bose particles produced by inflaton decay, such as parametric resonance, can be significant in the reheating process [4][5][6]. That means that semiclassical phenomena may play as important a role in reheating as they do in the structure formation. Of course, the eventual thermalized state will include modes with small occupation numbers, which are essentially quantal, but initial stages of the reheating process should admit a semiclassical description.However, semiclassical description of fluctuations produced by inflaton decay has not been obtained. The existing treatments of parametric amplification [4-6] employ the standard methods of analyzing particle production, based on Bogoliubov transformation. These methods allow one to take into account some of the backreaction effects of produced particles on the oscillating zero-momentum ͑k 0͒ mode, such as time dependence of the frequency of oscillations, but cannot reliably take into account many other nonlinear effects that become important certainly no later than the frequency change. These effects include scattering of produced particles off the k 0 mode, which knocks particles out of the k 0 state; rescattering of the produced particles, which populates nonresonant modes as well as returns particles back to k 0 (Bose condensation) [7], etc. We generically refer to these effects as rescattering; we will see that they begin as essentially classical interactions.Order of magnitude estimates of the amplitude squared of produced fluctuations ͑df͒ 2 at the end of the resonance stage were obtained in Refs. [4][5][6]. It is important to know ͑df͒ 2 more precisely, because in realistic inflationary models, its magnitude determines whether any symmetries are restored in the nonthermal regime after the reso...

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