Metric preheating and limitations of linearized gravity

During the preheating era after inflation, resonant amplification of quantu m field fluctuations takes place. Recently it has become clear that this mu st be accompanied by resonant amplification of scalar metric fluctuations, since the two are united by Einstein's equations. Furthermore, this "metric preheating" enhances particle production, and lends to gravitational resca ttering effects even at linens order. In multi-field models with strong pre heating (q much greater than 1), metric perturbations are driven non-linear , with the strongest amplification typically on super-Hubble scales (k --> 0). This amplification is causal, being due to the super-Hubble coherence o f the inflaton condensate, and is accompanied by resonant growth of entropy perturbations. The amplification invalidates the use of the linearized Ein stein field equations, irrespective of the amount of fine-tuning of the ini tial conditions. This has serious implications on all scales - from large a ngle cosmic microwave background (CMB) anisotropies to primordial black hol es. We investigate the (q,k) parameter space in a two-field model, and intr oduce the time to non-linearity, t(nl), as the timescale for the breakdown of the linearized Einstein equations. t(nl) is a robust indicator of resona nce behavior, showing the fine structure in q and k that one expects from a quasi-Floquet system, and we argue that t(nl) is a suitable generalization of the static Floquet index in an expanding universe. Backreaction effects are expected to shut down the linear resonances, but cannot remove the exi sting amplification, which threatens the viability of strong preheating whe n confronted with the CMB. Mode-mode coupling and turbulence tend to re-est ablish scale invariance, but this process is limited by causality and for s mall k the primordial scale invariance of the spectrum may be destroyed. We discuss ways to escape the above conclusions, including secondary phases o f inflation and preheating solely to fermions. The exclusion principle cons trains the amplification of metric perturbations significantly. Finally we rank known classes of inflation from strongest (chaotic and strongly couple d hybrid inflation) to weakest (hidden sector, warm inflation), in terms of the distortion of the primordial spectrum due to these resonances in prehe ating. (C) 1999 Elsevier Science B.V. All rights reserved.