  We present a manifestly local and general coordinate invariant formulation of
a nonlocal approach to the cosmological constant problem which has been
recently proposed by Carroll and Remmen. To do that, we need to introduce a
topological term involving a new 3-form gauge field. The equations of motion
for this new 3-form gauge field lead to a constant Lagrange multiplier
parameter and the resulting action becomes equivalent to that of Carroll and
Remmen. In our formulation, nonlocal informations are encoded via the procedure
of taking the space-time average at the stage of the equations of motion.
Consequently, our theory evades a no-go theorem by Weinberg and provides a new
solution to the cosmological constant problem in almost exactly the same way as
the original proposal by Carroll et al.
