Higgs inflation in metric and Palatini formalisms: Required suppression of higher dimensional operators

We investigate the sensitivity of Higgs(-like) inflation to higher dimensional operators in the nonminimal couplings and in the potential, both in the metric and Palatini formalisms. We find that, while inflationary predictions are relatively stable against the higher dimensional operators around the attractor point in the metric formalism, they are extremely sensitive in the Palatini one: for the latter, inflationary predictions are spoiled by $|\xi_4| \gtrsim 10^{-6}$ in the nonminimal couplings $(\xi_2 \phi^2 + \xi_4 \phi^4 + \cdots)R$, or by $|\lambda_6| \gtrsim 10^{-16}$ in the Jordan-frame potential $\lambda_4 \phi^4 + \lambda_6 \phi^6 + \cdots$ (both in Planck units). This extreme sensitivity results from the absence of attractor in the Palatini formalism. Our study underscores the challenge of realizing inflationary models with the nonminimal coupling in the Palatini formalism.