Note on Harada’s conformal Killing gravity

We show that ``gravity at cosmological distances: explaining the accelerating expansion without dark energy'' recently proposed by J. Harada [Phys. Rev. D 108, 044031 (2023)] is equivalent to the Einstein equation extended by the presence of an arbitrary conformal Killing tensor. This turns Harada's equations of third order in the derivatives of the metric tensor to second order, and offers a strategy of solution that covariantly shortcuts Harada's derivation and obtains both modified Friedmann equations. Another illustration is presented for the case of flat space and constant curvature.