Eur. Phys. J. C (2025) 85: 990
https://doi.org/10.1140/epjc/s10052-025-14737-2

Regular Article - Theoretical Physics

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

Department of Physics and Electronics, Christ University, 560029, Bangalore, India

^a kenath.arun@christuniversity.in

Received: 30 June 2025
Accepted: 3 September 2025
Published online: 15 September 2025

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 $\mathcal{O}(H_0)$, 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 $H_0=73.4\pm 0.6$ km/s/Mpc and ${\mathrm{\Omega }}_m=0.253\pm 0.007$, consistent with local expansion rate measurements. The best-fit scalar field parameters are ${\phi }_0\approx 0.027M_{\text{Pl}}$ and $\lambda \approx 0.010M_{\text{Pl}}$, corresponding to a present-day dark energy equation of state $w_0\approx -0.985$. While compatible with $\mathrm{\Lambda }$CDM within current observational bounds, the model satisfies GR recovery at low curvature and exhibits attractor-like behavior, thereby minimizing sensitivity to initial conditions.