Metric preheating and limitations of linearized gravity

TL;DR

This work shows that metric perturbations can be resonantly amplified during preheating in multi-field inflation, driven by strong non-gravitational couplings and entropy perturbations, which invalidates the linearized Einstein equations at relatively early times. By introducing the time-to-nonlinearity $t_{\rm nl}$ and performing detailed 2-field simulations, the authors demonstrate robust, super-Hubble growth of $\Phi_k$ that feeds back to enhance matter-field fluctuations, potentially altering the post-inflationary power spectrum and CMB signatures. The study argues that backreaction and nonlinear mode coupling will drive the system away from simple inflationary predictions, and outlines escape routes (secondary inflation, fermionic preheating, χ self-interactions, or initial-condition suppression) while emphasizing the need for nonlinear, gauge-invariant treatments and future quantum gravity considerations. Overall, metric preheating represents a fundamental limitation on the conventional perturbative picture and suggests new observational pathways to probe the early universe’s nonlinear dynamics.

Abstract

Recently it has become clear that the resonant amplification of quantum field fluctuations at preheating must be accompanied by resonant amplification of scalar metric perturbations, 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 \gg 1), metric perturbations are driven nonlinear, with the strongest amplification typically on super-Hubble scales (k \to 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 at all scales - from the 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 nonlinearity, t_{nl}, as the timescale for the breakdown of the linearized Einstein equations. 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. We discuss ways to escape the above conclusions, including secondary phases of inflation and preheating solely to fermions. 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.

Figures (16)

• Figure 1: Growth of $\ln \Phi_k$ versus $mt$, for $q = 8000$ with $\Phi \sim 10^{-3}$ initially. $\Phi$ is the gauge-invariant gravitational potential, $m$ is the inflaton mass, and $q$ is the resonance parameter, as defined in Sec. \ref{['sec:Preh']}. The specific model considered here is given by Eq. (\ref{['Vpc']}). The main plot is for $k = 0$, and the inset shows growth for $k = 20$; the former is a super-Hubble mode, while the latter is within the Hubble radius. This plot comes from linearized perturbation theory, and so cannot be used to describe the modes' behavior in the nonlinear regime. Note, however, the strong breaking of scale-invariance in the earliest, linear-regime phase: the two modes go nonlinear at very different times.
• Figure 2: Conceptual points of importance in understanding the origin of the metric perturbation resonances in strong preheating.
• Figure 3: Schematic plot illustrating how super-Hubble modes can be amplified without violating causality. To solve the horizon problem the inflaton must be correlated on vastly super-Hubble scales at the end of inflation, and hence this zero mode oscillates with a spacetime-independent phase. During preheating, fields at each spacetime event react only to physics in their causal past, which since the end of inflation may be very small. However, because the inflaton condensate is exactly the same over vastly larger regions than $H^{-1}$ at the end of inflation, super-Hubble modes can patch together the inflaton behavior in each region to reconstruct ("feel") the globally oscillating condensate and hence grow resonantly. Due to the isometries of the spacelike surfaces of constant $\phi$, all such patches are equivalent and can be mapped onto one another by a translation. Only once second-order backreaction effects destroy the coherence of the inflaton oscillations are these super-Hubble resonances weakened and perhaps ended.
• Figure 4: $\Phi$ vs $mt$ for $q = 5\times 10^3$, for the $k = 0$ mode. Note the initial resonance which invalidates the linearized equations of motion within a few oscillations. The linearized solution then damps away (after $mt \sim 300$) due to the expansion, but this cannot be taken as indicative of the evolution of the nonlinear solution. Interestingly there are two characteristic frequencies of oscillation of $\Phi_k$ after $mt \sim 250$ -- one high frequency and one low frequency. The inset shows the evolution of the inflaton condensate and the damping due to the expansion of the universe.
• Figure 5: The evolution of $\ln \delta\chi_k$ for $q = 8000$ and $k = 0$ (top), $k = 30$ (middle), and $k = 100$ (bottom). Note the significant resonant growth of the $k = 0$ mode.