Higgs inflation model with small non-minimal coupling constant

Abstract The Higgs sector of the Two-Measure Theory (TMT) extension of the electroweak SM (TMSM) is studied in the context of cosmology, where the only non-zero component φ of the cosmologically averaged Higgs field plays the role of the inflaton. The self-consistency of the system of equations obtained from the original action has the form of an algebraic constraint defining the scalar ζ , which is the ratio of two volume measures, as a function of the field φ and its first derivatives. The scalar ζ is present in all equations of motion and has a significant effect on the dynamics of the fields. After the transition in the equations of motion to the Einstein frame with the spatially flat Friedmann metric, it is convenient to describe the resulting system of equations using the action S eff and the Lagrangian L eff , which we call the TMT-effective action and the TMT-effective Lagrangian and from which these equations can be obtained. Due to the constraint, the original model parameters are converted in L eff into φ -dependent classical effective parameters. In particular, the effective potential U eff ( φ ) in L eff has the form U eff = λ/4 ξ 2 M P 4 · F( φ )·tanh 4 (√( ξ ) φ / M P ), where F ( φ ) is a smooth function equal to F ( φ ) ≈ 1/2 for φ > 6 M P . It is fundamentally important that the constant ξ of non-minimal coupling to the scalar curvature can be chosen small. If ξ = 1/6, then to ensure agreement with CMB observational data, the Higgs field self-coupling parameter λ in the original action must be of the order of ∼ 10 -11 . During cosmological evolution after the end of inflation, the decrease of φ leads to a change in the sign of the effective Higgs mass term in L eff . This TMSM effect provides an answer to the mystery of the Higgs potential structure and leads to spontaneous symmetry breaking. As φ approaches VEV, the scalar function ζ ( φ ) changes in such a way that the classical TMT-effective self-coupling parameter λ( ζ ( φ )) increases by 10 orders of magnitude compared to λ, which is necessary for the implementation of the GWS theory. Applying the model to the very beginning of the classical evolution of the Universe shows that under certain initial conditions, cosmological dynamics can begin with a “pathological” and even phantom regime preceding inflation. However, if evolution begins with normal dynamics, then it proceeds only as inflation, and the problem of initial conditions for the onset of inflation does not arise. The fermion preheating model is described as a preliminary study of preheatig after inflation. Mathematical and physical arguments in favor of using the TMT are presented.