Casimir Effect in the Rainbow Einstein's Universe

TL;DR

This paper explores how rainbow gravity modifies the Casimir effect in Einstein's universe by analyzing quantum vacuum fluctuations with altered dispersion relations, using zeta function regularization methods.

Contribution

It introduces a novel analysis of the Casimir effect within rainbow gravity models, extending the understanding of quantum vacuum behavior in modified dispersion relation scenarios.

Findings

Quantum vacuum fluctuations are altered by rainbow gravity modifications.

Regularization using Epstein-Hurwitz and Riemann zeta functions is effective.

Results differ from standard General Relativity predictions.

Abstract

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.