Asymptotically Safe Starobinsky Inflation

Abstract

We revisit Starobinsky inflation in a quantum gravitational context, by means of the exact Renormalisation Group (RG). We calculate the non-perturbative beta functions for Newton's `constant' G and the dimensionless R^2 coupling, and show that there exists an attractive UV fixed point where the latter one vanishes but not the former one, and we provide the corresponding beta functions. The smallness of the R^2 coupling, required for agreement with inflationary observables, is naturally ensured by its vanishing at the UV fixed point, ensuring the smallness of the primordial fluctuations, as well as providing a theoretical motivation for the initial conditions needed for successful inflation in this context. We discuss the corresponding RG dynamics, showing both how inflationary and classical observations define the renormalisation conditions for the couplings, and also how the UV regime is connected with lower energies along the RG flow. Finally, we discuss the consistency of our results when higher order curvature corrections are included, and show that they are robust to the inclusion of R^3 corrections.

14 pages, 4 figures. v.3: This version matches the one published in PRD. The results and conclusions remain the same. Some clarifying comments, new references, and three new figures have been added. A new section investigating the significance of higher-order operators has been introduced

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