The Preheating Stage on The Starobinsky Inflation after ACT

TL;DR

The paper reexamines Starobinsky inflation under ACT data, showing that fitting the 68% CL requires $N \approx 75.5$ and yields a low reheating temperature around $T_{\rm reh} \sim 10^4$ GeV. Efficient preheating in this setup necessitates a spectator field with non-minimal coupling $\xi$ of order ~10 and specific initial conditions, with a tachyonic preheating onset rather than zero-crossing production. Reheating is dominated by the end of preheating: a final burst producing $\chi$ followed by $\chi\to\psi$ decays, which gives the observed low $T_{\rm reh}$; perturbative decays to bosons are strongly disfavored, while fermionic channels remain possible but suboptimal. The parameter space includes viable sets that could yield collider-detectable daughter fields, but the mechanism may fail if ACT’s central $n_s$ shifts such that $T_{\rm reh}$ falls below ~GeV, indicating the need for further study and possible model extensions.

Abstract

In this paper, we reinvestigate the Starobinsky inflation model and its reheating features in light of the recent ACT results. To make the Starobinsky model consistent with the ACT data at the $68\%$ confidence level, the number of e-folds must increase while the reheating temperature decreases. We find that the Starobinsky model requires a spectator field to achieve efficient preheating. The preheating stage and the reheating temperature must be significantly adjusted to accommodate the lower temperature. In this paper, the favored non-minimal coupling of the produced particles is approximately $10$ or slightly lower. We also present viable parameter sets that fit the preferred reheating mechanism in this model. For certain parameter choices, the daughter fields could potentially be detected in future collider experiments such as the LHC or the ILC. Furthermore, our proposed mechanism can reproduce the lower reheating temperature, but it fails when the temperature falls below $1$ GeV.

Figures (4)

• Figure 1: The plot of $\phi$ with time $t$. The unit of $\phi$ is $M_p$ while the unit of $t$ is in $M_p^{-1}$.
• Figure 2: The growth of $\chi_k$ by the resonance production. We fixed $M=9.07 \times 10^{-6}M_p$, $M_p=1$, $k_\chi=10^{-8}M_p$, $m_\chi=10^{-8}M_p$, and $a=1$. The solid-red represents to the $\chi_k(0)=0$, The dashed-blue represents to the $\chi_k(0)=10^{-5}M_p$, and The solid-black represents to the $\chi_k(0)=10^{-2.5}M_p$. The varied $\xi$ is depicted in the corresponding panels: panel (A) uses $\xi=1$, panel (B) uses $\xi=4$, panel (C) uses $\xi=7$, and panel (D) uses $\xi=10$. The $\chi_k$ is in a unit of $M_p$ while $t$ is in a unit of $M_p^{-1}$.
• Figure 3: The comparison of analytical result (solid-red) and numerical result (solid-black) in $\chi_k^2$. We used amplification $1.1 \times 10^{1.8}$ on the numerical result to match the analytical ones. In this plot, we used $\xi=10$, $k_\chi=10^{-8}M_p$, $m_\chi=10^{-8}M_p$, $\chi_k(0)=10^{2.5}M_p$ and $\Dot{\chi}_k=0$.
• Figure 4: Mathieu instability region related to the semi-analytical result depicted in Eq. \ref{['mathieu']}. The right legend corresponds to the value of $\mu_p$. The white region corresponds to the stable condition.