Coexistence of matter dominated and accelerating solutions in f ( G ) gravity

Working within the theory of modified Gauss-Bonnet gravity, we show that Friedmann-Lemaitre-Robertson-Walker-like power-law solutions only exist for a very special class of f(G) theories. Furthermore, we point out that any transition from decelerated to accelerated expansion must pass through G=0, and no function f(G) that is differentiable at this point can admit both a decelerating power-law solution and any accelerating solution. This strongly constrains the cosmological viability of f(G) gravity, since it may not be possible to obtain an expansion history of the Universe which is compatible with observations. We explain why the same issue does not occur in f(R) gravity and discuss possible caveats for the case of f(G) gravity.