Abstract
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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