Higgs-R2 inflation - full slow-roll study at tree-level

We consider Higgs inflation with an alpha R-2 term. It adds a new scalar degree of freedom, which leads to a two-field model of inflation. We do a complete slow-roll analysis of the three-dimensional parameter space of the R-2 coefficient alpha, the non-minimal coupling xi and the Higgs self-coupling lambda. We find three classes of inflationary solutions, but only pure R-2 and attractor solutions fit observations. We find that pure Higgs inflation is impossible when the R-2 term is present regardless of how small alpha is. However, we can have Higgs-like inflation, where the amplitude of the perturbations does not depend on alpha and the predictions as a function of e-folds are the same as in Higgs inflation, although the inflationary trajectory is curved in field space. The spectral index is 0.939 < n(R) < 0.967, and constraining it to the observed range, the tensor-to-scalar ratio varies from 3.8 x 10(-3) to the maximum allowed by observations, 0.079. Observational constraints on isocurvature perturbations contribute to these limits, whereas non-Gaussianity is automatically in the range allowed by observations.