Lowering the self-coupling of the scalar field in a generalized Higgs inflation

We study cosmological dynamics of a generalized Higgs inflation. By expanding the action up to the second and third order in the small perturbations, we study the primordial perturbation and its non-Gaussian distribution. We study the non-Gaussian feature in both the equilateral and orthogonal configurations. By adopting a quartic potential, we perform a numerical analysis on the model's parameter space and compare the results with Planck2015 observational data. To obtain some observational constraint, we focus on the self-coupling and the non-minimal coupling parameters. We show that, in the presence of the non-minimal coupling and the Galileon-like interaction, the self-coupling parameter can be reduced to the order of $10^{-6}$ which is much larger than the value that CMB normalization suggests for this self-coupling.