Classical and quantum initial conditions for Higgs inflation

We investigate whether Higgs inflation can occur in the Standard Model starting from natural initial conditions or not. The Higgs has a non-minimal coupling to the Ricci scalar. We confine our attention to the regime where quantum Einstein gravity effects are small in order to have results that are independent of the ultraviolet completion of gravity. At the classical level we find no tuning is required to have successful Higgs inflation, provided the initial homogeneity condition is satisfied. On the other hand, at the quantum level we obtain that the renormalization for large non-minimal coupling requires an additional degree of freedom, unless a tuning of the initial values of the running parameters is made. In order to see that this effect may change the predictions we finally include such degree of freedom in the field content and show that Starobinsky's R2R2 inflation dominates over Higgs inflation.