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Register a new userPerturbative Reheating in the Mixed Higgs-$R^2$ Model
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Minxi He
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The preheating process in the mixed Higgs-$ R^2 $ model has been investigated in depth recently, but the analysis of perturbative reheating is still missing. In this paper, we discuss the effect of perturbative decay during (p)reheating in this model. It is shown that perturbative decay can play an important role throughout the whole reheating process. Depending on the model parameters, perturbative decay can affect different stages of the reheating. We study the perturbative reheating with and without the presence of early preheating stage, and calculate the reheating temperature and the duration of the whole perturbative process. We find that the detail of the early preheating stage may not affect the final reheating temperature while it can affect the number of e-folds of reheating.
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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.
We study $R^2$-Higgs inflation in a model with two Higgs doublets. The context is the general two Higgs doublet model where the Higgs sector of the Standard Model is extended by an additional Higgs doublet. We first discuss the required inflationary dynamics in this two Higgs doublet model, which includes four scalar fields, in the covariant formalism allowing a nonminimal coupling between the Higgs-squared and the Ricci scalar $R$, as well as the $R^2$ term. We find that the parameter space favored by $R^2$-Higgs inflation requires nearly degenerate $m_mathsf{H}$, $m_A$ and $m_{mathsf{H}^pm}$, where $mathsf{H}$, $A$, and $mathsf{H}^pm$ are the extra CP even, CP odd, and charged Higgs bosons in the general two Higgs doublet model taking renormalization group evolutions of the parameters into account. Discovery of such heavy scalars at the Large Hadron Collider are possible if they are in the sub-TeV mass range. Indirect evidences may also emerge at the LHCb and Belle-II experiments, however, to probe the quasi degenerate mass spectra one would likely require future lepton colliders such as the International Linear Collider and the Future Circular Collider.
We propose that the Standard Model (SM) Higgs is responsible for generating the cosmological perturbations of the universe by acting as an isocurvature mode during a de Sitter inflationary stage. In view of the recent ATLAS and CMS results for the Higgs mass, this can happen if the Hubble rate during inflation is in the range $(10^{10}- 10^{14})$ GeV (depending on the SM parameters). Implications for the detection of primordial tensor perturbations through the $B$-mode of CMB polarization via the PLANCK satellite are discussed. For example, if the Higgs mass value is confirmed to be $m_h=125.5$ GeV and $m_t, alpha_s$ are at their central values, our mechanism predicts tensor perturbations too small to be detected in the near future. On the other hand, if tensor perturbations will be detected by PLANCK through the $B$-mode of CMB, then there is a definite relation between the Higgs and top masses, making the mechanism predictive and falsifiable.
In the context of the Palatini formalism of gravity with an $R^{2}$ term, a $phi^{2}$ potential can be consistent with the observed bound on $r$ whilst retaining the successful prediction for $n_{s}$. Here we show that the Palatini $phi^{2} R^2$ inflation model can also solve the super-Planckian inflaton problem of $phi^{2}$ chaotic inflation, and that the model can be consistent with Planck scale-suppressed potential corrections. If $alpha gtrsim 10^{12}$, where $alpha$ is the coefficient of the $R^2$ term, the inflaton in the Einstein frame, $sigma$, remains sub-Planckian throughout inflation. In addition, if $alpha gtrsim 10^{20}$ then the predictions of the model are unaffected by Planck-suppressed potential corrections in the case where there is a broken shift symmetry, and if $alpha gtrsim 10^{32}$ then the predictions are unaffected by Planck-suppressed potential corrections in general. The value of $r$ is generally small, with $r lesssim 10^{-5}$ for $alpha gtrsim 10^{12}$. We calculate the maximum possible reheating temperature, $T_{R;max}$, corresponding to instantaneous reheating. For $alpha approx 10^{32}$, $T_{R; max}$ is approximately $10^{10}$ GeV, with larger values of $T_{R;max}$ for smaller $alpha$. For the case of instantaneous reheating, we show that $n_{s}$ is in agreement with the 2018 Planck results to within 1-$sigma$, with the exception of the $alpha approx 10^{32}$ case, which is close to the 2-$sigma$ lower bound. Following inflation, the inflaton condensate is likely to rapidly fragment and form oscillons. Reheating via inflaton decays to right-handed neutrinos can easily result in instantaneous reheating. We determine the scale of unitarity violation and show that, in general, unitarity is conserved during inflation.
We analyse Starobinsky inflation in the presence of the Brout Englert Higgs (BEH) boson with a non-minimal coupling to the Ricci scalar, $R$. The latter induces a coupling of the massive scaleron associated with the $R^2$ term to the BEH boson and this leads to a radiative correction to the BEH mass that must be fine tuned to keep the scalar light. For the case of $R^2$ driven inflation this requires a high level of fine tuning of order 1 part in $10^{8}$; for the case of Higgs inflation it is very much greater. We consider a scale invariant extension of the $R^2$/Higgs model and find that for $R^2$ driven inflation but not for Higgs inflation the required fine tuning is significantly reduced to one part in $10^{3-4}$. We consider the vacuum stability of the fine tuned model and its reheating and dilaton abundance after inflation. We also discuss possible gravitational wave signals associated with the model and the constraint on the mass of scalar or fermion dark matter candidates if they are produced by the gravitational couplings of the scalaron.
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