  A modified Einstein-Gauss-Bonnet gravity in four dimensions where the
quadratic Gauss-Bonnet term is coupled to a scalar field is considered. The
field equations of the model are obtained by variational methods by making use
of the constrained-first order formalism covering both pseudo-Riemannian and
non-Riemannian cases. In the pseudo-Riemannian case, the Lagrange multiplier
forms, which impose the vanishing torsion constraint, are eliminated in favor
of the remaining fields and the resulting metric field equations are expressed
in terms of the double-dual curvature 2-form. In the non-Riemannian case with
torsion, the field equations are expressed in terms of the pseudo-Riemannian
quantities by a perturbative scheme valid for a weak coupling constant. It is
shown that, for both cases, the model admits a maximally symmetric de-Sitter
solution with nontrivial scalar field. Minimal coupling of a Dirac spinor to
the Gauss-Bonnet modified gravity is also discussed briefly.
