Cosmological and Thermodynamic Insights into Barrow-Ricci-Gauss-Bonnet Holographic Dark Energy in the Symmetric Teleparallel Framework of f(Q) Gravity

• We develop a Barrow-Ricci-Gauss-Bonnet holographic dark energy (BRGB-HDE) model within the symmetric teleparallel f(Q) gravity framework. • The reconstructed equation of state parameter exhibits quintessence-like behavior and asymptotically approaches the cosmological constant boundary at late times. • A numerical reconstruction of the f(Q) function reveals strong early-time geometric corrections that gradually weaken during cosmic evolution. • The generalized second law of thermodynamics is satisfied throughout the evolution, confirming the thermodynamic consistency of the model. • The squared speed of sound remains positive for suitable values of the Barrow parameter, ensuring dynamical stability of the reconstructed model. In this work, we develop a Barrow-Ricci-Gauss-Bonnet holographic dark energy (BRGB-HDE) model in the framework of symmetric teleparallel f ( Q ) gravity. The main motivation of this study is that quantum gravity corrections and modified gravity effects both may have important role in explaining the late-time accelerated expansion of the universe. By including Barrow entropy with the deformation parameter Δ, the usual holographic dark energy density becomes modified. Also, extra geometrical terms coming from the Ricci scalar and Gauss-Bonnet invariant are taken into account. We further study the cosmological behaviour of the model by considering interaction between dark energy and dark matter. We establish a correspondence between the BRGB-HDE density and the effective energy density in f ( Q ) gravity, which allows us to reconstruct the functional form of f ( Q ). In addition, we examine the thermodynamic consistency of the model by testing the generalized second law of thermodynamics (GSLT) within the Barrow entropy formalism. The results show that the total entropy remains non-decreasing throughout the cosmic evolution. For dynamical stability, it is observed that for proper values of the Barrow parameter Δ, the model stays stable during the cosmic evolution. The equation of state shows quintessence type behaviour and slowly moves towards the cosmological constant boundary at late time. Therefore, the present BRGB-HDE model in f ( Q ) gravity gives a physically reasonable and thermodynamically consistent explanation of the accelerated expansion of the universe. Therefore, the present BRGB-HDE model in f ( Q ) gravity gives a physically reasonable and thermodynamically consistent explanation of the accelerated expansion of the universe. The framework further provides a field-theoretic bridge between modified gravity and particle cosmology, capturing quantum vacuum effects through geometric reconstruction.