  We compute the Zero Point Energy in a spherically symmetric background
distorted at high energy as predicted by \textit{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. With the help of a canonical
decomposition, we find that the relevant contribution to one loop is given by
the graviton quantum fluctuations around the given background. By means of a
variational approach based on gaussian trial functionals, 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. A final discussion on the connection of our result with the
observed cosmological constant is also reported.
