Power-laws f(R) theories are cosmologically unacceptable

In a recent paper,¹ we have shown that f(R) = R + μR ⁿ modified gravity dark energy models are not cosmologically viable because during the matter era that precedes the accelerated stage the cosmic expansion is given by a ∼ t^1/2 rather than a ∼ t ^2/3, where a is a scale factor and t is the cosmic time. A recent work by Capozziello et al.² criticized our results presenting some apparent counter-examples to our claim in f(R) = μRⁿ models. We show here that those particular Rⁿ models can produce an expansion as a ∼ t^2/3 but this does not connect to a late-time acceleration. Hence, though acceptable f(R) dark energy models might exist, the Rⁿ models presented in Capozziello et al. are not cosmologically viable, confirming our previous results in Ref. 1.