We consider general linear Higgs-sigma models as ultra-violet completions of the Higgs inflation. We introduce general higher curvature terms beyond Einstein gravity and recast them into a class of linear Higgs-sigma models in the scalar-dual formulation where conformal symmetry is manifest. Integrating out the sigma field in this class of linear sigma models, we obtain the same Higgs inflation Lagrangian of non-linear sigma model type in the effective theory. We show that the successful inflation for sigma field singles out the sigma-field potential derived from the R2 term and the tracker solution for dark energy at late times can be realized for the Rp+1 term with −1 < p < 0. We also discuss the implications of Higgs-sigma interactions for the inflation and the vacuum stability in the Standard Model.

We consider general linear Higgs-sigma models as ultra-violet completions of the Higgs inflation. We introduce general higher curvature terms beyond Einstein gravity and recast them into a class of linear Higgs-sigma models in the scalar-dual formulation where conformal symmetry is manifest. Integrating out the sigma field in this class of linear sigma models, we obtain the same Higgs inflation Lagrangian of non-linear sigma model type in the effective theory. We show that the successful inflation for sigma field singles out the sigma-field potential derived from the R 2 term and the tracker solution for dark energy at late times can be realized for the R p+1 term with −1 < p < 0. We also discuss the implications of Higgs-sigma interactions for the inflation and the vacuum stability in the Standard Model.

We study the post-inflationary dynamics for reheating and freeze-in dark matter in the Higgs-R2 inflation model. Taking the perturbative approach for reheating, we determine the evolution of the temperature for radiation bath produced during reheating and determine the maximum and reheating temperatures of the Universe. Adopting a singlet scalar dark matter with a conformal non-minimal coupling and a vanishing Higgs-portal coupling, we discuss the freeze-in production of dark matter both from the non-thermal scattering during reheating and the thermal scattering after reheating. We find that thermal scattering is dominant for dark matter production in our model due to the high reheating temperature. The reheating temperature in our model is determined dominantly by the Higgs condensate to be up to about 1014 GeV and dark matter with masses up to about 109 GeV can be produced with a correct relic density.

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We propose a new construction of the supergravity inflation as an UV completion of the Higgs-R2 inflation. In the dual description of R2-supergravity, we show that there appear dual chiral superfields containing the scalaron or sigma field in the Starobinsky inflation, which unitarizes the supersymmetric Higgs inflation with a large non-minimal coupling up to the Planck scale. We find that a successful slow-roll inflation is achievable in the Higgs-sigma field space, but under the condition that higher curvature terms are introduced to cure the tachyonic mass problems for spectator singlet scalar fields. We also discuss supersymmetry breaking and its transmission to the visible sector as a result of the couplings of the dual chiral superfields and the non-minimal gravity coupling of the Higgs fields.