The big constant out, the small constant in

Some time ago, Tseytlin has made an original and unusual proposal for an action that eliminates an arbitrary cosmological constant. The form of the proposed action, however, is strongly modified by gravity loop effects, ruining its benefit. Here I discuss an embedding of Tseytlin's action into a broader context, that enables to control the loop effects. The broader context is another universe, with its own metric and dynamics, but only globally connected to ours. One possible Lagrangian for the other universe is that of unbroken AdS supergravity. A vacuum energy in our universe does not produce any curvature for us, but instead increases or decreases the AdS curvature in the other universe. I comment on how to introduce the accelerated expansion in this framework in a technically natural way, and consider the case where this is done by the self-accelerated solutions of massive gravity and its extensions.