Loop-corrected scalar potentials and late-time acceleration in f(R) gravity

Abstract

We construct an analytic f(R) gravity model that unifies early-time inflation with late-time cosmic acceleration within a single covariant framework. At high curvature, the model reproduces a Starobinsky-like inflationary plateau, while at low curvature it asymptotes to a stable dark energy-dominated phase. In the scalar-tensor representation, this construction yields a hilltop-type potential in the Jordan frame, which maps to an exponential potential in the Einstein frame. To account for radiative effects, we introduce a logarithmic correction to the Einstein-frame potential inspired by one-loop effective field theory, producing a late-time flattening without requiring fine-tuning. The resulting scalaron dynamics reduce the effective mass to O(H_0), inducing a thawing regime that deviates from a cosmological constant at the sub-percent levels. A joint background likelihood analysis using Pantheon+SH0ES and BAO+CC datasets (within the CPL parametrization) yields H_0 = 73.4+-0.6 km/s/Mpc and Omega_m = 0.253+-0.007, consistent with local expansion rate measurements. The best-fit scalar field parameters are phi_0 \approx 0.027\,M_Pl and lambda \approx 0.010\,M_Pl, corresponding to a present-day dark energy equation of state w_0 \approx -0.985. While compatible with LambdaCDM within current observational bounds, the model satisfies GR recovery at low curvature and exhibits attractor-like behavior, thereby minimizing sensitivity to initial conditions.

45 pages, 6 figures, 3 appendix

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