In this study, we realize a unified solution of F(R, T~2) gravity in the context of the spatially flat Friedmann-Robertson-Walker universe, where R is the Ricci curvature scalar and T~2 = T_(μv) T~(μv) is the scalar constructed from the square of the energy-momentum tensor. We observe that these solutions describe a transition from deceleration eras of the universe to late-time quintessential dark energy in a unified form.
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