Strong coupling in Higgs inflation at high energies hinders a joint description of inflation, reheating and low-energy dynamics. The situation may be improved with a proper UV completion of the model. A well-defined self-consistent way is to introduce an R 2 -term into the action. In this modified model the strong coupling scale returns back to the Planck scale, which justifies the use of the perturbative methods in studies of the model dynamics after inflation. We investigate the reheating of the post-inflationary Universe, which involves two highly anharmonic oscillators strongly interacting with each other: homogeneous Higgs field and scalaron. We observe that in interesting regions of model parameter space these oscillations make longitudinal components of the weak gauge bosons tachyonic, triggering instant preheating at timescales much shorter than the Hubble time. The weak gauge bosons are heavy and decay promptly into light Standard Model particles, ensuring the onset of the radiation domination era right after inflation.Email addresses: Fedor.Bezrukov@manchester.ac.uk (Fedor Bezrukov), gorby@ms2.inr.ac.ru (Dmitry Gorbunov), christopher.shepherd-3@postgrad.manchester.ac.uk (Chris Shepherd), tokareva@ms2.inr.ac.ru (Anna Tokareva)

We use a semiclassical lattice approach to perform the first nonlinear study of preheating in R2-healed Higgs inflation, in the “R2-like” regime where the curvature-squared coupling β and nonminimal coupling ξ of the Higgs field contribute similarly to the CMB scalar perturbations. Preheating occurs first through tachyonic production of Higgs bosons, and later scattering off the homogeneous inflaton field. We generalise our results for the parameter range 1.1× 109<β<1.8× 109 to “Higgs-like” parameters with smaller β, where observables saturate the bound of instantaneous preheating. All predictions for the spectral index and tensor-to-scalar ratio lie within the 1σ region of measurements by the Planck satellite, but a future ground-based experiment optimised for 21 cm tomography may be able to discriminate the mixed Higgs-curvature inflation from the pure Higgs and R2 theories.

A recent calculation of the multi-Higgs boson production in scalar theories with spontaneous symmetry breaking has demonstrated the fast growth of the cross section with the Higgs multiplicity at sufficiently large energies, called "Higgsplosion". It was argued that "Higgsplosion" solves the Higgs hierarchy and fine-tuning problems. In our paper we argue that: a) the formula for "Higgsplosion" has a limited applicability and inconsistent with unitarity of the Standard Model; b) that the contribution from "Higgsplosion" to the imaginary part of the Higgs boson propagator cannot be re-summed in order to furnish a solution of the Higgs hierarchy and fine-tuning problems.