Casimir Effect in the Rainbow Einstein's Universe

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.Comment: 15 pages, 1 figure. To appear in Europhysics Letter

A Note on the Robustness of Pair Separations Methods in Cosmic Topology

The pair separations statistical methods devised to detect the topology of the universe rely on the accurate knowledge of the three-dimensional positions of the cosmic sources. The determination of these positions, however, involves inevitable observational uncertainties. The only significant (measurable) sign of a nontrivial topology in PSH's was shown to be spikes. We briefly report our results concerning the sensitivity of the topological spikes in the presence of the uncertainties in the positions of the cosmic sources, which arise from uncertainties in the values of the density parameters.Comment: To appear in the Proc. of 10th Marcel Grossmann Meeting on General Relativity. Latex2e, World Scientific proc. style files, 2 figs., 4 page