| Summary: | Abstract In this work, the $$f({\mathcal {G}},T)$$ f ( G , T ) theory of gravity is recast in terms of the $$\phi $$ ϕ and $$\psi $$ ψ fields within the scalar-tensor formulation, where $${\mathcal {G}}$$ 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 $$f({\mathcal {G}},T)$$ f ( G , T ) theory is successfully reconstructed for the early and late time approximations with the corresponding potentials. The procedure of recovering the $$f({\mathcal {G}},T)$$ 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 $$f({\mathcal {G}},T)$$ f ( G , T ) gravity which can be viewed as an extension of the well-established scalar Einstein–Gauss–Bonnet gravity.
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