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 (H₀) 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 H₀ = 73. 4 0. 6 H 0 = 73. 4 ± 0. 6 km/s/Mpc and ₘ = 0. 253 0. 007 Ω m = 0. 253 ± 0. 007, consistent with local expansion rate measurements. The best-fit scalar field parameters are ₀ 0. 027\, MPl φ 0 ≈ 0. 027 M Pl and 0. 010\, MPl λ ≈ 0. 010 M Pl, corresponding to a present-day dark energy equation of state w₀ -0. 985 w 0 ≈ - 0. 985. While compatible with Λ CDM within current observational bounds, the model satisfies GR recovery at low curvature and exhibits attractor-like behavior, thereby minimizing sensitivity to initial conditions.