  We compute the Zero Point Energy in a spherically symmetric background
distorted at high energy as predicted by Gravity's Rainbow. In this context we
setup a Sturm-Liouville problem with the cosmological constant considered as
the associated eigenvalue. The eigenvalue equation is a reformulation of the
Wheeler-DeWitt equation. We find that the ordinary divergences can here be
handled by an appropriate choice of the rainbow's functions, in contrast to
what happens in other conventional approaches.
