Metric preheating and limitations of linearized gravity

Abstract

During the preheating era after inflation, resonant amplification of quantum field fluctuations takes place. Recently it has become clear that this must 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 leads to gravitational rescattering effects even at linear order. In multi-field models with strong preheating ( q≫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 of the inflaton condensate, and is accompanied by resonant growth of entropy perturbations. The amplification invalidates the use of the linearized Einstein field equations, irrespective of the amount of fine-tuning of the initial conditions. This has serious implications on all scales – from large-angle cosmic microwave background (CMB) anisotropies to primordial black holes. We investigate the ( q, k) parameter space in a two-field model, and introduce 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 resonance 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 existing amplification, which threatens the viability of strong preheating when confronted with the CMB. Mode–mode coupling and turbulence tend to re-establish scale invariance, but this process is limited by causality and for small k the primordial scale invariance of the spectrum may be destroyed. We discuss ways to escape the above conclusions, including secondary phases of inflation and preheating solely to fermions. The exclusion principle constrains the amplification of metric perturbations significantly. Finally we rank known classes of inflation from strongest (chaotic and strongly coupled hybrid inflation) to weakest (hidden sector, warm inflation), in terms of the distortion of the primordial spectrum due to these resonances in preheating.