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

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 Ω ₘ = 0.253 ± 0.007 Ω m = 0.253 ± 0.007 , consistent with local expansion rate measurements. The best-fit scalar field parameters are φ ₀ ≈ 0.027\,MPl φ 0 ≈ 0.027 M Pl and λ ≈ 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 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.