Gauss-Bonnet modified gravity and energy conditions

In this work we explore the viability of modified gravity models within the f ( G, T ) framework, where G denotes the Gauss-Bonnet invariant and T the trace of the energy-momentum tensor. The study analyzes three functional forms of f ( G, T ) by examining the constraints imposed by the weak energy condition (WEC) to ensure the physical viability of the resulting spacetimes. By incorporating T , the theory introduces curvature-matter couplings that may effectively arise from quantum corrections to the gravitational action, making the framework relevant to particle cosmology and early-universe physics. We identify parameter regions where the WEC is satisfied and show that the simplest model, f ( G , T ) = f 1 ( G ) + γ T k , yields results consistent with the latest Planck 2024 and DES Y3 data. The analysis demonstrates that the f ( G, T ) approach provides a viable bridge between high-energy particle effects and large-scale cosmic acceleration.