In Remmen and Carroll 2013, it was claimed that in the spatially flat cosmological case there exists a unique conserved measure (up to normalization) on the $(\varphi ,\dot{\varphi })$ phase space for scalar field with $m^2{\varphi }^2$ potential by finding a unique solution to the differential equation (44) (in Remmen and Carroll 2013) in the low-energy regime. In Remmen and Carroll 2014, it was also claimed that a unique solution to the same differential equation was found in the high-energy regime and using this solution the authors calculated the expected total number of $e$-folds of inflation. In this comment, we reanalyze the differential equation (44) and obtain general solutions both in the low-energy and high-energy regime, which can include the solution in Remmen and Carroll 2013 and the solution in Remmen and Carroll 2014 as a special case in the corresponding energy regime. In this way, we find that following the constructions in the 2013 article there actually exist infinitely many nonequivalent conserved measures for the scalar-field cosmology with $m^2{\varphi }^2$ potential on the $(\varphi ,\dot{\varphi })$ phase space. Moreover, through specific calculations, we also show that different choices of measures can lead to quite different predictions of the expected total number of $e$-folds of inflation.

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