Occurrence of Tachyonic Preheating in the Mixed Higgs-$R^2$ Model

TL;DR

This paper investigates the conditions and efficiency of tachyonic preheating in the mixed Higgs-$R^2$ inflation model, highlighting the necessary fine-tuning of parameters for successful particle production after inflation.

Contribution

It provides a detailed analysis of the parameter conditions, analytical estimates, and fine-tuning requirements for tachyonic preheating in the mixed Higgs-$R^2$ model, extending previous understanding.

Findings

Efficient tachyonic preheating can occur in both Higgs-like and $R^2$-like regimes.

Severe fine-tuning of parameters is required, especially in the $R^2$-like regime.

Parameter tuning is less severe in the Higgs-like regime with large scalaron mass.

Abstract

It has recently been suggested that at the post-inflationary stage of the mixed Higgs-$R^2$ model of inflation efficient particle production can arise from the tachyonic instability of the Higgs field. It might complete the preheating of the Universe if appropriate conditions are satisfied, especially in the Higgs-like regime. In this paper, we study this behavior in more depth, including the conditions for occurrence, analytical estimates for the maximal efficiency, and the necessary degree of fine-tuning among the model parameters to complete preheating by this effect. We find that the parameter sets that cause the most efficient tachyonic instabilities obey simple laws in both the Higgs-like regime and the $R^2$-like regime, respectively. We then estimate the efficiency of this instability. In particular, even in the deep $R^2$-like regime with a small non-minimal coupling, this effect is strong enough to complete preheating although a severe fine-tuning is required among the model parameters. We also estimate how much fine-tuning is needed to complete preheating by this effect. It is shown that the fine-tuning of parameters for the sufficient particle production is at least $ < \mathcal{O}(0.1) $ in the deep Higgs-like regime with a large scalaron mass, while it is more severe $\sim {\cal O}(10^{-4})-{\cal O}(10^{-5})$ in the $R^2$-like regime with a small non-minimal coupling.