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

We consider Higgs inflation with an α R² 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 R² coefficient α, the non-minimal coupling ξ and the Higgs self-coupling λ. We find three classes of inflationary solutions, but only pure R² and attractor solutions fit observations. We find that pure Higgs inflation is impossible when the R² term is present regardless of how small α is. However, we can have Higgs-like inflation, where the amplitude of the perturbations does not depend on α 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 3.8×10⁻³ 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.