  We introduce a novel theory of gravity based on the inverse of the Ricci
tensor, that we call the anticurvature tensor. We derive the general equations
of motion for any Lagrangian function of the curvature and anticurvature
scalars. We then demonstrate a no-go theorem: no Lagrangian that contains terms
linear in any positive or negative power of the anticurvature scalar can drive
an evolution from deceleration to acceleration, as required by observations.
This effectively rules out many realizations of this theory, as we illustrate
in detail in a particular case. Finally, we speculate on how to circumvent the
no-go theorem.
