Coexistence of matter dominated and accelerating solutions in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="script">G</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>gravity

Working within the theory of modified Gauss-Bonnet gravity, we show that Friedmann-Lema\^{\i}tre-Robertson-Walker--like power-law solutions only exist for a very special class of $f(\mathcal{G})$ theories. Furthermore, we point out that any transition from decelerated to accelerated expansion must pass through $\mathcal{G}=0$, and no function $f(\mathcal{G})$ 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 $f(\mathcal{G})$ 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 $f(\mathcal{G})$ gravity.

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