Reconstruction of f(Q,T) Gravity from Logarithmically Corrected Ricci-Gauss-Bonnet Holographic Dark Energy
The current paper reports an investigation on the cosmological and thermodynamic behaviour of an $f(Q,T)$ modified-gravity framework in which the gravitational Lagrangian is written as $f(Q,T)=f(Q)+λT$, with $Q$ denoting the non-metricity scalar and $T$ the trace of the energy-momentum tensor. The modified Friedmann equations are formulated in terms of an effective Dark Energy sector, and the corresponding equation of state and squared speed of sound are examined for a phenomenological polynomial form of $f(Q)$. A power-law background is constrained using 32 Cosmic Chronometer measurements. The resulting background is then used to study the effective Dark Energy dynamics and its classical stability in the redshift range considered. In this study, we further construct a generalized Ricci-Gauss-Bonnet holographic Dark Energy model with logarithmic entropy corrections based on the Nojiri-Odintsov prescription and establish a correspondence between its energy density and the effective Dark Energy density of the $f(Q,T)$ framework. The full function $f(Q,T)$ is then given by adding the trace contribution $λT$. Finally, the thermodynamic behaviour of the reconstructed model is studied at the apparent horizon with the Nojiri-Odintsov entropy motivated by \textit{Phys. Rev. D} \textbf{105}, 044042 (2022) and the Gibbs relation. The entropy evolution obtained from the compact background description is also found to be consistent with that obtained from the reconstructed effective-fluid formulation, with only small numerical residuals. These results provide a consistent framework for examining the connection between generalized holographic dark energy, reconstructed $f(Q,T)$ gravity, and cosmic thermodynamics.