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We introduce conformal coupling of the Standard Model Higgs field to gravity and discuss the subsequent modification of R²-inflation. The main observation is a lower temperature of reheating which happens mostly through scalaron decays into gluons due to the conformal (trace) anomaly. This modifies all predictions of the original R²-inflation. To the next-to-leading order in slow roll parameters we calculate amplitudes and indices of scalar and tensor perturbations produced at inflation. The results are compared to the next-to-leading order predictions of R²-inflation with minimally coupled Higgs field and of Higgs-inflation. We discuss additional features in gravity wave signal that may help to distinguish the proposed variant of R²-inflation. Remarkably, the features are expected in the region available for study at future experiments like BBO and DECIGO. Finally, we check that (meta) stability of electroweak vacuum in the cosmological model is consistent with recent results of searches for the Higgs boson at LHC.
Gorbunov et al. (Tue,) studied this question.