Study of Barrow holographic dark energy in the framework of Gauss–Bonnet cosmology

Abstract In this work, we propose a new approach within modified f ( R , G ) gravity to explore a possible explanation for the accelerated expansion of the universe. Given the tensions in cosmological parameters, we investigate this class of theories, which unifies geometric corrections from both the Ricci scalar R and the Gauss–Bonnet term G . By studying the $$f(R,G) = \alpha R^n {G}^m$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>,</mml:mo> <mml:mi>G</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mi>α</mml:mi> <mml:msup> <mml:mi>R</mml:mi> <mml:mi>n</mml:mi> </mml:msup> <mml:msup> <mml:mrow> <mml:mi>G</mml:mi> </mml:mrow> <mml:mi>m</mml:mi> </mml:msup> </mml:mrow> </mml:math> model in conjunction with the Barrow holographic dark energy (BHDE) model, we provide a generalized framework to address dark energy (DE) through both curvature-based modifications and quantum-gravitational microstructure effects, thereby avoiding the need for a cosmological constant. Additionally, we estimate parameters using the most recent observational data, such as direct measurements of the Hubble parameter, BAO, and Type Ia supernova. Our findings demonstrate that the model offers a theoretical framework for explaining the accelerated expansion of the cosmos and late-time cosmic evolution. The evolution of the effective equation of state parameter, the deceleration parameter (DP), and the cosmographic parameters are thoroughly examined based on the best fit values of the model parameters. The classical stability of the BHDE model has also been addressed. The model provides a different way to study DE in modified gravity theories, despite the extra complexity it introduces.