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We compute the Zero Point Energy in a spherically symmetric backgrounddistorted at high energy as predicted by \textit{Gravity's Rainbow}. In thiscontext we setup a Sturm-Liouville problem with the cosmological constantconsidered as the associated eigenvalue. The eigenvalue equation is areformulation of the Wheeler-DeWitt equation. With the help of a canonicaldecomposition, we find that the relevant contribution to one loop is given bythe graviton quantum fluctuations around the given background. By means of avariational approach based on gaussian trial functionals, we find that theordinary divergences can here be handled by an appropriate choice of therainbow's functions, in contrast to what happens in other conventionalapproaches. A final discussion on the connection of our result with theobserved cosmological constant is also reported.

Modified Dispersion Relations lead to a finite Zero Point Gravitational Energy