Résumé
Working within the theory of modified Gauss-Bonnet gravity, we show that FLRW-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 compare to the case of f (R)-gravity, and discuss possible caveats for the case of f (G)-gravity.