Reconstructing $f(R)$ gravity from Viaggiu Holographic Dark Energy under Hubble, Event Horizon and Granda Oliveros cutoffs

Abstract

This work explores the reconstruction of $f(R)$ gravity within the framework of newly proposed Viaggiu holographic dark energy (VHDE), which incorporates entropy corrections due to the dynamical nature of cosmological horizons. By implementing a correspondence between VHDE and curvature-induced energy density, we generate explicit forms of $f(R)$ for different infrared cutoffs, namely the Hubble horizon, future event horizon, and Granda Oliveros cutoff. The resulting models are analyzed graphically through the cosmological parameters such as the equation of state and deceleration parameter, revealing a successful description of the transition from decelerated to accelerated expansion. The viability of the reconstructed models is further examined through stability conditions and local gravity constraints, that yields the nature of the models as free from ghost and tachyonic instabilities and demonstrates VHDE-inspired $f(R)$ gravity model as a consistent and flexible geometric framework for explaining the late-time cosmic acceleration of the Universe.