Dynamics of tachyonic preheating after hybrid inflation

TL;DR

The paper tackles tachyonic preheating at the end of hybrid inflation by combining analytic growth analyses with nonperturbative lattice simulations. It shows that the unstable-mode band is set by $k_*$, which scales as $k_*\approx(2mg\dot\varphi)^{1/3}$, and that the spinodal time $t_{\rm spin}$ governs late-time dynamics; defect densities follow the same scaling as in thermal phase transitions. The inflaton's oscillations drive local energy-density hotspots that temporarily restore symmetry, providing a mechanism for rapid energy transfer from the inflaton and strong damping of homogeneous oscillations. These results are demonstrated across two and three dimensions and in both global and gauge theories, highlighting the robustness of tachyonic preheating as an efficient reheating channel with potential cosmological consequences.

Abstract

We study the instability of a scalar field at the end of hybrid inflation, using both analytical techniques and numerical simulations. We improve previous studies by taking the inflaton field fully into account, and show that the range of unstable modes depends sensitively on the velocity of the inflaton field, and thereby on the Hubble rate, at the end of inflation. If topological defects are formed, their number density is determined by the shortest unstable wavelength. Finally, we show that the oscillations of the inflaton field amplify the inhomogeneities in the energy density, leading to local symmetry restoration and faster thermalization. We believe this explains why tachyonic preheating is so effective in transferring energy away from the inflaton zero mode.

Figures (10)

• Figure 1: Power spectra of the $\chi$ field measured at various times after the transition for $g=10^{-4}$, $\dot\varphi=1.0$. The solid and dotted lines show the results of the numerical simulations and of the analytical approximation in Eq. (\ref{['equ:predPk']}), respectively. From bottom to top, the lines correspond to the instants when $\langle\chi^2\rangle=1$, 10, 100, 1000 and 10000.
• Figure 2: Power spectra of the $\chi$ field at two different times after the transition for $g=10^{-4}$ and various different values of $\dot\varphi$. The dashed and solid lines corresponds to the instants when $\langle\chi^2\rangle=100$ and $10000$, respectively, and the four different curves correspond to values $\dot\varphi=0.1$, $1$, $10$ and $100$ from bottom to top. The dotted vertical lines show the cutoff scales $k_*$ calculated in Eq. (\ref{['equ:esthatk']}) (ignoring the logarithmic factor).
• Figure 3: The ratio of the measured wall length $L_{\rm wall}$ to the prediction in Eq. (\ref{['equ:predLwall']}) as a function of the velocity $\dot\varphi$. The solid lines are for $g=10^{-4}$ and, from top to bottom, correspond to the times when $\langle\chi^2\rangle=10^3$, $10^4$, $10^5$ and when $\langle\varphi\rangle=0$. The dashed line with open circles corresponds to $g=10^{-3}$ and $\langle\chi^2\rangle=10^3$.
• Figure 4: An example of a network of domain walls after the transition. Blue (dark grey) and red (medium grey) regions correspond to positive and negative values of $\chi$, and $\chi$ vanishes at the green (light grey) domain walls.
• Figure 5: The amplification of the oscillations by an inhomogeneous mass term. The dotted line shows the unperturbed oscillation, and the solid and dashed lines show the full numerical solution and the analytical approximation in Eq. (\ref{['equ:sol_deltasigma']}) for the field at the origin with the perturbed mass term (\ref{['equ:pertmass']}) and the parameter values $D=1$, $\varphi=1$, $\epsilon=0.5$, $\Delta=10$ and $M_0^2=1$.