Standard Model Higgs boson mass from inflation: two loop analysis

We extend the analysis of \cite{Bezrukov:2008ej} of the Standard Model Higgs inflation accounting for two-loop radiative corrections to the effective potential. As was expected, higher loop effects result in some modification of the interval for allowed Higgs masses m_min<m_H<m_max, which somewhat exceeds the region in which the Standard Model can be considered as a viable effective field theory all the way up to the Planck scale. The dependence of the index n_s of scalar perturbations on the Higgs mass is computed in two different renormalization procedures, associated with the Einstein (I) and Jordan (II) frames. In the procedure I the predictions of the spectral index of scalar fluctuations and of the tensor-to-scalar ratio practically do not depend on the Higgs mass within the admitted region and are equal to n_s=0.97 and r=0.0034 respectively. In the procedure II the index n_s acquires the visible dependence on the Higgs mass and and goes out of the admitted interval at m_H below m_min. We compare our findings with the results of \cite{DeSimone:2008ei}.
Comment: 24 paged, 9 figures. Journal version (typos fixed, expanded discussions)