  Inspired by Verlinde's idea, some modified versions of entropic gravity have
appeared in the literature. Extending them in a unified formalism, we derive
the generalized gravitational equations accordingly. From gravitational
equations, the energy-momentum conservation law and cosmological equations are
investigated. The covariant conservation law of energy-momentum tensor severely
constrains viable modifications of entropic gravity. A discrepancy arises when
two independent methods are applied to the homogeneous isotropic universe,
posing a serious challenge to modified models of entropic gravity.
