Preheating in New Inflation

TL;DR

This paper analyzes nonperturbative preheating in new inflation by combining analytic estimates with lattice simulations. It shows that tachyonic preheating and parametric resonance jointly drive rapid decay of the homogeneous inflaton for symmetry-breaking scales $v$ below about $0.01\,M_p$, typically within ~5 oscillations, followed by a slower perturbative decay into other fields. Lattice results reveal a sequence where long-wavelength tachyonic amplification gives way to a parametric-resonance peak in the spectrum, with rescattering producing an IR-flat distribution and a cutoff near $k\sim v$. The authors estimate the perturbative late-stage reheating temperature, finding $T_r$ to be relatively low (e.g., $\lesssim 10^7$ GeV for $v\sim10^{-3}M_p$ and $g^2\lesssim\lambda$), and discuss conditions under which higher $T_r$ could occur, highlighting key distinctions between new inflation and the chaotic/hybrid scenarios.

Abstract

During the last ten years a detailed investigation of preheating was performed for chaotic inflation and for hybrid inflation. However, nonperturbative effects during reheating in the new inflation scenario remained practically unexplored. We do a full analysis of preheating in new inflation, using a combination of analytical and numerical methods. We find that the decay of the homogeneous component of the inflaton field and the resulting process of spontaneous symmetry breaking in the simplest models of new inflation usually occurs almost instantly: for the new inflation on the GUT scale it takes only about 5 oscillations of the field distribution. The decay of the homogeneous inflaton field is so efficient because of a combined effect of tachyonic preheating and parametric resonance. At that stage, the homogeneous oscillating inflaton field decays into a collection of waves of the inflaton field, with a typical wavelength of the order of the inverse inflaton mass. This stage usually is followed by a long stage of decay of the inflaton field into other particles, which can be described by the perturbative approach to reheating after inflation. The resulting reheating temperature typically is rather low.

Figures (7)

• Figure 1: Mean value of the inflaton field $\langle\phi\rangle$ (zero mode) for $v=10^{-1} M_p$. A horizontal line indicates the field value below which the potential is tachyonic (negative mass squared). The amplitude of the field here and in other figures is given in units of $v$, whereas the time $t$ is given in units $m^{-1}=\left(\sqrt{\lambda} v\right)^{-1}$, where $m$ is the mass of the scalar field near the minimum of the effective potential.
• Figure 2: Squared mean $\langle\phi\rangle^2$ and variance $\langle\delta\phi^2\rangle$ of the inflaton field for $v=10^{-3} M_p$. A horizontal line indicates the field value below which the potential is tachyonic (negative mass squared). As one can clearly see form this figure, the oscillations of the homogeneous component of the scalar field $\phi$ are completely damped out after the first 5 oscillations, whereas the variance remains much smaller than 1, in units of $v$. This means that the process of spontaneous symmetry breaking in this scenario completes within 5 oscillations.
• Figure 3: Spectra of occupation number $n_k$ as a function of momentum $k$ at different times for $v=10^{-3} M_p$.
• Figure 4: Growth of a fluctuation in the peak ($k \approx 0.58$). The lower curves show the evolution of the zero mode and the upper curves show the occupation number $n_k$ of this mode. The solid (black) curves show results from LATTICEEASY. The thin (red) curves show results from a Mathematica calculation in which the zero mode was evolved with no backreaction. These results confirm our expectations that the growth of the modes with $k \sim 0.5$ occur due to parametric resonance practically independently of the tachyon preheating.
• Figure 5: This figure is the same as figure \ref{['levsmath']} except showing only the lattice results and zoomed in to show features more clearly. As we see, the exponential growth of the occupation numbers occurs each time when the average value of the scalar field becomes much smaller than $v$.