Fractional holographic dark energy driven reconstruction of f(Q) gravity and its cosmological implications

Abstract

To explain the late-time acceleration of the Universe, we reconstruct an f(Q) gravity model inspired by fractional holographic dark energy (FHDE) with the Hubble horizon as the infrared cutoff. This reconstructed f(Q) gravity model shows a geometrically motivated dark energy component and naturally recovers general relativity in the appropriate limit. The free parameters of the model are constrained using the latest DESI baryon acoustic oscillation (BAO) data, previous BAO compilations, and cosmic chronometer datasets through a Markov Chain Monte Carlo analysis. The reconstructed Hubble parameter H(z) exhibits excellent consistency with observational data, with high values of R2 and low values of , Akaike information criterion, and Bayesian information criterion, confirming the model’s strong statistical performance relative to ΛCDM. With current deceleration parameter and a transition redshift –0.46, the dynamical diagnostics show a smooth transition from a decelerated to an accelerated phase. While the Om(z) diagnostic exhibits a negative slope, indicating that the model is not ΛCDM like in behaviour, Statefinder diagnostics shows the model to have quintessence like behaviour. The analysis of classical energy conditions shows that the WEC, DEC, and NEC are satisfied throughout the cosmic evolution, with a violation of the SEC at lower-redshift, which is consistent with late-time acceleration. Linear homogeneous perturbation analysis further confirms the model’s dynamical stability. Conclusively, the FHDE-inspired reconstructed f(Q) gravity provides a stable, observationally compatible, and geometrically motivated alternative to ΛCDM, that successfully describes the late-time cosmic acceleration within the symmetric teleparallel framework.