Agegraphic dark energy with fractional entropy: Implications for cosmological evolution

This work revisits the agegraphic dark energy (ADE) model by associating fractional entropy with the apparent horizon. This reveals the extent to which quantum-gravitational effects deform the horizon. The thermodynamic-gravity conjecture modifies the entropy expression, leading to changes in the energy density of ADE and the Friedmann equations. Based on this relationship, we have utilized modified fractional cosmology to investigate the cosmological implications of ADE and demonstrate how the exponent \(\delta \) affects the evolution of cosmic parameters. Depending on the value of \(\delta \), the equation of state (EoS) parameter \(\omega _{\text {DE}}\) make transition from the quintessence range (\(-1< \omega _{\text {DE}} < -1/3\)) to the phantom regime \((\omega _{\text {DE}} < -1)\), resulting in a shift from early deceleration to late time acceleration. Furthermore, the stability, theoretical and observational analyses of both the old and the new ADE models are discussed. All ADE results are reproduced in standard cosmology when \(\delta = 2\).