  In a recently proposed theory, the cosmological constant (CC) does not curve
spacetime in our universe, but instead gets absorbed into another universe
endowed with its own dynamical metric, nonlocally coupled to ours. Thus, one
achieves a long standing goal of removing entirely any cosmological constant
from our universe. Dark energy then cannot be due to a cosmological constant,
but must be obtained via other mechanisms. Here we focus on the scenario in
which dark energy is due to massive gravity and its extensions. We show how the
metric of the other universe, that absorbs our CC, also gives rise to the
fiducial metric known to be necessary for the diffeomorphism invariant
formulation of massive gravity. This is achieved in a framework where the other
universe is described by 5D AdS gravity, while our universe lives on its
boundary and is endowed with dynamical massive gravity. A non-dynamical
pullback of the bulk AdS metric acts as the fiducial metric for massive gravity
on the boundary. This framework also removes a difficulty caused by the quantum
strongly coupled behavior of massive gravity at the Lambda3 scale: in the
present approach, the massive gravity action does not receive any loop-induced
counterterms, despite being strongly coupled.
