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 \varphi(t) of the cosmologically averaged Higgs field plays the role of the inflaton. The self-consistency of the system of equations has the form of an algebraic constraint defining the scalar \zeta equal to the ratio of two volume measures, as a function of \varphi. The \zeta is present in all equations of motion and has a significant effect on the dynamics. After the transition in the equations of motion to the Einstein frame, the resulting system of equations is described by the TMT-effective action S_{eff} and Lagrangian L_{eff}. Due to the constraint, the original model parameters are converted into \varphi-dependent classical effective parameters. The effective potential is U_{eff}=\frac{\lambda{4\xi^2}M_P^4\cdotF(\varphi)\cdot\tanh^4\bigl(\frac{\sqrt{\xi}\varphi}{M_P}\bigr), where F(\varphi)\approx \frac{1}{2} for \varphi >\sqrt{6}M_P. If \xi=1/6, then to ensure agreement with CMB observational data, the Higgs field self-coupling model parameter \lambda must be \sim10^{-11}. After the end of inflation, the decrease of \varphi leads to a change in the sign of the effective Higgs mass term, that leads to SSB. As \varphi approaches VEV, \zeta changes in such a way that the TMT-effective \lambda increases by 10 orders of magnitude to the value in the GWS theory. Applying the model to the very beginning of the classical evolution of the Universe shows that cosmological dynamics can begin with a "pathological" and even phantom regime. 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 preheating after inflation.