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Late-time Cosmology of scalar field assisted $f(\mathcal{G})$ gravity

In this work we present the late-time behaviour of the Universe in the context of Einstein-Gauss-Bonnet gravitational theory. The theory involves a scalar field, which represents low-effective quantum corrections, assisted by a function $f(\mathcal{G})$ solely depending from the Gauss-Bonnet topological invariant $\mathcal{G}$. It is considered that the dark energy serves as the impact of all geometric terms, which are included in the gravitational action and the density of dark energy acts as a time dependent cosmological constant evolving with an infinitesimal rate and driving the Universe into an accelerating expansion. We examine two cosmological models of interest. The first involves a canonical scalar field in the presence of a scalar potential while the second, involves a scalar field which belongs to a generalized class of theories $f(ϕ,X)$ namely the k-essence scalar field in the absence of scalar potential. As it is proved, the aforementioned models are in consistency with the latest Planck data and in relatively good agreement with the $Λ$CDM standard cosmological model. The absence of dark energy oscillations at the early stages of matter dominated era, which appear in alternative scenarios of cosmological dynamics in the context of modified $f(R)$ gravitational theories, indicates an advantage of the theory for the interpretation of late-time phenomenology.