Two-loop corrections to Starobinsky-Higgs inflation

Higgs inflation and R-2 inflation (Starobinsky model) are two limits of the same quantum model, hereafter called Starobinsky-Higgs. We analyze the two-loop action of the Higgs-like scalar phi in the presence of (1) nonminimal coupling (xi) and (2) quadratic curvature terms. The latter are generated at the quantum level with phi-dependent couplings ((alpha) over tilde) even if their tree-level couplings (a) are tuned to zero. Therefore, the potential always depends on both Higgs field phi and scalaron rho; hence, multifield inflation is a quantum consequence. The effects of the quantum (one-and two-loop) corrections on the potential (W) over cap (phi, rho) and on the spectral index are discussed, showing that the Starobinsky-Higgs model is, in general, stable in their presence. Two special cases are also considered: first, for a large xi in the quantum action, one can integrate phi and generate a "refined" Starobinsky model which contains additional terms xi(2)R(2)ln(p)(xi vertical bar R vertical bar/mu(2)), p = 1, 2 (mu is the subtraction scale). These generate corrections linear in the scalaron to the "usual" Starobinsky potential and a "running" scalaron mass. Second, for a small fixed Higgs field phi(2) << M-p(2)/xi and a vanishing classical coefficient of the R-2 term, we show that "usual" Starobinsky inflation is generated by quantum corrections alone, for a suitable nonminimal coupling (xi).