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Gauss-Bonnet-dilatonic coupling in four dimension plays an important role toexplain late time cosmic evolution. However, this term is an outcome of lowenergy string effective action and thus ought to be important in the earlyuniverse too. Unfortunately, phase-space formulation of such a theory does notexist in the literature due to branching. We therefore consider a modifiedtheory of gravity, which contains a nonminimally coupled scalar-tensor sectorin addition to higher order scalar curvature invariant term withGauss-Bonnet-dilatonic coupling. Such an action unifies early inflation withlate-time cosmic acceleration. Quantum version of the theory is alsowell-behaved.

History of cosmic evolution with modified Gauss-Bonnet-dilatonic coupled term