Occurrence of tachyonic preheating in the mixed Higgs-R² model

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 < O(0.1) in the deep Higgs-like regime with a large scalaron mass, while it is more severe ∼ O(10 −4) − O(10 −5) in the R 2-like regime with a small non-minimal coupling.

Construction of inflationary scenarios with the Gauss–Bonnet term and nonminimal coupling

“…For example, the R 2 -inflation [1,7,[52][53][54] and the Higgs-driven inflation [21] have almost the same values of inflationary parameters [55]. The simple reason why the Starobinsky R 2 inflation and the Higgs-driven inflation produce the same predictions for the inflationary parameters n s and r is the possibility to omit in the slow-roll approximation the Higgs gradient term in the Jordan frame action [47,56]. Note that each of these models includes only one arbitrary parameter.…”

Critical point Higgs inflation in the Palatini formulation

“…Higher order curvature terms can also have a large effect on the inflationary dynamics and restore perturbative unitarity, as well as change the RG running [45,96,102,[105][106][107][108][109][110][111][112][113][114][115][116][117][118][119][120][121][122][123][124]. In the Palatini case not all such terms introduce new degrees of freedom, so they have a less drastic impact on both the classical potential and loop corrections, meaning the formulation is more robust to corrections [125].…”

The $$R^2$$-Higgs inflation with two Higgs doublets

“…The perturbative unitarity of the Higgs inflation can be restored up to the Planck scale by introducing additional scalars at the inflationary scale [31,32] or, by scalaron degree of freedom due to the presence of R 2 term (R 2 -Higgs inflation) in the Jordan frame [33] (see also for e.g. [34][35][36][37][38][39][40][41][42][43]).…”