The hybrid cosmology in the scalar-tensor representation of f($G$, T) gravity

In this work, the f($G$, T) theory of gravity is recast in terms of the ϕ and ψ fields within the scalar-tensor formulation, where $G$ is the Gauss-Bonnet term and T denotes the trace of the energy-momentum tensor. The general aspects of the introduced reformulation are discussed and the reconstruction of the cosmological scenarios is presented, focusing on the so-called hybrid evolution. As a result, the scalar-tensor f($G$, T) theory is successfully reconstructed for the early and late time approximations with the corresponding potentials. The procedure of recovering the f($G$, T) theory in the original formulation is performed for the late time evolution and a specific quadratic potential. The scalar-tensor formulation introduced herein not only facilitates the description of various cosmic phases but also serves as a viable alternative portrayal of the f($G$, T) gravity which can be viewed as an extension of the well-established scalar Einstein-Gauss-Bonnet gravity.