  Gauss-Bonnet-dilatonic coupling in four dimension plays an important role to
explain late time cosmic evolution. However, this term is an outcome of low
energy string effective action and thus ought to be important in the early
universe too. Unfortunately, phase-space formulation of such a theory does not
exist in the literature due to branching. We therefore consider a modified
theory of gravity, which contains a nonminimally coupled scalar-tensor sector
in addition to higher order scalar curvature invariant term with
Gauss-Bonnet-dilatonic coupling. Such an action unifies early inflation with
late-time cosmic acceleration. Quantum version of the theory is also
well-behaved.
