Comment on "covariant version of Verlinde's emergent gravity"

Following Verlinde's recent heuristic construction or emergent gravity, Hossenfelder wrote down the Lagrangian capturing some aspects of this theory. We point out that there is an error in calculations whose consequence is that a cosmological de Sitter space solution is not recovered from this Lagrangian. We correct this error in order to obtain the desired solution. We also show that small perturbations around the de Sitter space grow, which implies that this state is not stable. However, the presence of matter and radiation might, in principle, provide stability.