Modified f(G) gravity models with curvature-matter coupling
  A modified f(G) gravity model with coupling between matter and geometry is
proposed, which is described by the product of the Lagrange density of the
matter and an arbitrary function of the Gauss-Bonnet term. The field equations
and the equations of motion corresponding to this model show the
non-conservation of the energy-momentum tensor, the presence of an extra-force
acting on test particles and the non-geodesic motion. Moreover, the energy
conditions and the stability criterion at de Sitter point in the modified f(G)
gravity models with curvature-matter coupling are derived, which can degenerate
to the well-known energy conditions in general relativity. Furthermore, in
order to get some insight on the meaning of these energy conditions, we apply
them to the specific models of f(G) gravity and the corresponding constraints
on the models are given. In addition, the conditions and the candidate for
late-time cosmic accelerated expansion in the modified f(G) gravity are studied
by means of conditions of power-law expansion and the equation of state of
matter less than -1/ 3 .
