Self-resonance preheating in deformed attractor models: oscillon formation and evolution

TL;DR

This work analyzes self-resonance preheating in a deformed α-attractor T-model with a Gaussian near-minimum feature, using linear Floquet analysis and nonlinear lattice simulations. It shows that the feature reshapes resonance bands but does not much affect gradient-energy transfer during resonance, while post-resonance evolution of gradient energy and oscillon properties becomes strongly $h$-dependent: larger $|h|$ yields more, smaller oscillons with shorter lifetimes and a suppressed late-time gravitational-wave signal. The gravitational-wave spectrum is dominated by the resonance stage and is largely suppressed once oscillons form, with the low-frequency part remaining nearly unchanged and the high-frequency tail significantly modified. These results imply that potential features can qualitatively modify reheating dynamics and the expansion history, offering new insights into oscillon formation and cosmological signatures, though a full reheating treatment requires external couplings and higher-resolution simulations.

Abstract

It is well known that, in potentials that are quadratic near the minimum but shallower away, such as small-$α$ ($\ll M_P^2$) attractors, the inflaton condensate fragments into localized compact objects known as oscillons during self-resonance preheating. In this work we investigate the self-resonance in deformed $α$-attractor T-model with a Gaussian feature near the minimum, distant from inflation's end. Linear analysis reveals altered resonance bands and deformed Floquet charts dependent on feature parameters. In fully nonlinear lattice simulations, we find that the gradient energy transfer is largely independent of the potential feature parameter $h$. In contrast, after resonance terminates, the subsequent evolution of gradient energy becomes strongly dependent on $h$. Statistical analysis reveals that models with the potential feature produce larger number of smaller oscillons, with a reduced energy stored in these objects, increasingly suppressed as the magnitude of $h$ grows. By tracking the total energy and the gradient energy contained in oscillons, we find that in models with nonzero $h$ oscillons are systematically shorter-lived, with this effect strengthening for larger $h$. The gravitational wave emission is dominated by the resonance stage and is strongly suppressed once oscillons form. Potential features leave the low-frequency spectrum largely unchanged but significantly modify the high-frequency tail. Although a complete reheating description requires external couplings and higher-resolution simulations, clear qualitative differences of cosmic expansion history already emerge within our simulated time window. These results highlight the important role of potential features in shaping reheating dynamics and their cosmological implications, and provide a deeper understanding of preheating dynamics and the properties of oscillons.

Figures (19)

• Figure 1: Plots of the deformed T-model potential for the parameters in table . The end of inflation $\phi_{\mathrm{i}}$ is defined by $\epsilon_V(\phi_{\mathrm{i}})=1$. The blue shaded regions are those with $V"<0$ indicating the field space where tachyonic instability may occur.
• Figure 2: The violation of adiabatic condition for parametric resonance and the tachyonic instability condition for deformed T-model ($h=0.2$).
• Figure 3: Upper two rows: The Floquet charts for the models with $P_1$ and $P_2$ set of parameters. Lower two rows: The Floquet exponents of different modes evaluated at a fixed field value $\phi=0.015\,M_P$, as well as those of the mode $k=0.5\,m$ evaluated at different field values. Note that these results are obtained with cosmic expansion neglected.
• Figure 4: Comparison of the field evolution result obtained from the nonlinear equation () and the homogeneous equation (), and the r.m.s $\sqrt{\langle \delta\tilde{\phi}^2 \rangle}$ (green), for the parameter set $P_1$ with $h=0.4$.
• Figure 5: Dimensionless power spectra of scalar fluctuations. The plots correspond to $h=0$ (upper left), $h=0.4$ (upper right), $h=-0.4$ (lower left), and the comparison of spectra.