Two-loop corrections to Starobinsky-Higgs inflation

Abstract

Higgs inflation and R2 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 φ in the presence of (1) nonminimal coupling (ξ) and (2) quadratic curvature terms. The latter are generated at the quantum level with φ-dependent couplings (α) even if their tree-level couplings (α) are tuned to zero. Therefore, the potential always depends on both Higgs field φ and scalaron ρ; hence, multifield inflation is a quantum consequence. The effects of the quantum (one- and two-loop) corrections on the potential W^(φ,ρ) 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 ξ in the quantum action, one can integrate φ and generate a "refined" Starobinsky model which contains additional terms ξ2R2lnp(ξ|R|/μ2), p=1, 2 (μ 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 φ2Mp2/ξ and a vanishing classical coefficient of the R2 term, we show that "usual" Starobinsky inflation is generated by quantum corrections alone, for a suitable nonminimal coupling (ξ).