Minimal Higgs inflation

We consider a possibility that the Higgs field in the Standard Model (SM) serves as an inflaton when its value is around the Planck scale. We assume that the SM is valid up to an ultraviolet cutoff scale \Lambda, which is slightly below the Planck scale, and that the Higgs potential becomes almost flat above \Lambda. Contrary to the ordinary Higgs inflation scenario, we do not assume the huge non-minimal coupling, of O(10^4), of the Higgs field to the Ricci scalar. We find that \Lambda must be less than 5*10^{17}GeV in order to explain the observed fluctuation of the cosmic microwave background, no matter how we extrapolate the Higgs potential above \Lambda. The scale 10^{17}GeV coincides with the perturbative string scale, which suggests that the SM is directly connected with the string theory. For this to be true, the top quark mass is restricted to around 171GeV, with which \Lambda can exceed 10^{17}GeV. As a concrete example of the potential above \Lambda, we propose a simple log type potential. The predictions of this specific model for the e-foldings N_*=50--60 are consistent with the current observation, namely, the scalar spectral index is n_s=0.977--0.983 and the tensor to scalar ratio 0<r<0.012--0.010. Other parameters, dn_s/dlnk, n_t, and their derivatives, are also consistent.