Massless Metric Preheating

TL;DR

The paper demonstrates analytically that super-Hubble gauge-invariant metric perturbations can undergo exponential growth during preheating in massless, conformally invariant multi-field models by reducing the perturbation equations to a generalized Lamé form and applying Floquet analysis. It shows that the conventional conserved-ζ picture can fail in large regions of parameter space, and that backreaction from homogeneous inflaton and decay products couples metric and field fluctuations to produce synchronized, large-amplitude growth that ends only when the inflaton dynamics change. The work further links the initial conditions for preheating to the inflationary evolution, derives the post-preheating χ power spectrum, and identifies a divided g^2/λ parameter space with distinct cosmological implications, including potential imprints on the CMB for certain ranges. Finally, it highlights how strong self-interactions in decay products, when metric perturbations are included, can enhance rather than suppress resonance channels, affecting relic abundances of particles produced during preheating.

Abstract

Can super-Hubble metric perturbations be amplified exponentially during preheating ? Yes. An analytical existence proof is provided by exploiting the conformal properties of massless inflationary models. The traditional conserved quantity ζis non-conserved in many regions of parameter space. We include backreaction through the homogeneous parts of the inflaton and preheating fields and discuss the role of initial conditions on the post-preheating power-spectrum. Maximum field variances are strongly underestimated if metric perturbations are ignored. We illustrate this in the case of strong self-interaction of the decay products. Without metric perturbations, preheating in this case is very inefficient. However, metric perturbations increase the maximum field variances and give alternative channels for the resonance to proceed. This implies that metric perturbations can have a large impact on calculations of relic abundances of particles produced during preheating.

Figures (4)

• Figure 1: Floquet index, $\mu_{\kappa}$, instability chart. White represents $\mu_{\kappa} = 0$, darker greys represent increasing $\mu_{\kappa}$ (left). $\mu_{\kappa}$ vs $\kappa^2 \equiv k^2/\lambda\varphi_0^2$ for $g^2/\lambda = 2$ (right). Both plots are for the generalized Lamé equation given by Eq. (\ref{['qchi']}) with the RHS set to zero and $\tilde{\varphi} = cn(x,1/\sqrt{2})$.
• Figure 2: The gauge-invariant metric perturbations $\tilde{\Phi}$ and $\tilde{Q}^{\chi}_k$, $\tilde{Q}^{\varphi}_k$ for the super-Hubble mode $\kappa^2 = 10^{-20}$ and $g^2/\lambda = 2$. Note that $\tilde{\Phi}_k$ grows with Floquet index $\mu \simeq 0.357$, much larger than the maximum possible in preheating neglecting metric perturbations which is bounded for all values of $g^2/\lambda$ to be less than or equal to $0.238$. Inset: $\tilde{\zeta}_k$ for $g^2/\lambda = 2$ ($\tilde{\zeta}_k$ exponentially growing) and $g^2 = 0$ ($\tilde{\zeta}_k$ constant).
• Figure 3: The field $\tilde{\chi}$ and the gauge-invariant metric perturbations $\tilde{\Phi}_k$, $\tilde{Q}^{\chi}_k$ and $\tilde{Q}^{\varphi}_k$ for $\kappa^2 =10^{-20}$ and $g^2/\lambda = 2$. Note the onset of backreaction in $\tilde{\chi}$ at $x \simeq 50$ and the synchronisation in the metric perturbations for $x \geq 50$. Inset: The evolution of the inflaton condensate $\tilde{\varphi}$: note the drop in amplitude and increase in oscillation frequency at $x \simeq 50$ and $135$.
• Figure 4: Evolution of metric perturbations with $\tilde{\chi}$ self-interaction: (a) $\tilde{\Phi}_k$ (b) $\tilde{Q}^{\chi}_k$ (c) $\tilde{Q}^{\varphi}_k$ and the $\tilde{\chi}$ field, for $\lambda_{\chi} = 10^{2}\lambda$, $\kappa^2 = 10^{-20}$ and $g^2/\lambda = 2$. While self-interaction stops $\tilde{\chi}$ from growing, it fails to stop exponential growth of the metric perturbations. Inset:$\tilde{\Phi}_k$ evolution with all terms on the RHS of Eq's (\ref{['qphi']},\ref{['qchi']}) set to zero, and $\lambda_{\chi} = 10^{-8} \lambda$. The apparent shut-off of the resonance is an artifact due to neglect of backreaction and coupling between $\tilde{Q}^{\varphi}_k$ and $\tilde{Q}^{\chi}_k$.