  In the present paper we investigate the effects caused by the modification of
the dispersion relation obtained by solving the Klein-Gordon equation in the
closed Einstein's universe in the context of rainbow's gravity models. Thus, we
analyse how the quantum vacuum fluctuations of the scalar field are modified
when compared with the results obtained in the usual General Relativity
scenario. The regularization, and consequently the renormalization, of the
vacuum energy is performed adopting the Epstein-Hurwitz and Riemann's zeta
functions.
