Casimir effect in the rainbow Einstein's universe

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.

Landau levels in the presence of a cosmic string in rainbow gravity

“…the rainbow functions, which was not totally the case of the non-relativistic analysis. This behavior is in accordance with previous analysis of the effect of rainbow function on energy levels in other contexts [30].…”

“…Studies of Landau levels in the spacetime of a cosmic string (disclination) has been conducted in Refs [25][26][27][28][29]. 2 The Landau levels have previously been considered in the context of modified theories of gravity, basically those ones involving the Generalized Uncertainty Principle, and can be 2 The effect of rainbow functions on energy levels has also been analyzed in the context of the Casimir effect in the Einstein universe [30] and for the Dirac oscillator in [31].…”

Dirac oscillator in the cosmic string spacetime in the context of gravity’s rainbow

“…where we shall consider a first order parameter for our purposes. These rainbow functions fit the requirement of a constant velocity of light and solves the horizon problem puzzle [9,10,12,22]. In this first scenario of gravity's rainbow, described by the rainbow functions in Eq.…”

“…Let us now construct a scenario of the cosmic string gravity's rainbow by using the following rainbow functions [9,10,12,22]:…”

“…The semi-classical approach of Gravity's Rainbow has been used, for instance, to investigate Cosmological and Astrophysical phenomena in a variety of contexts ranging from Friedmann-Robertson-Walker Universe [9][10][11][12], black hole thermodynamics [13][14][15][16][17] to neutron stars' properties [18], massive scalar field in the Schwarzschild metric [19][20][21] and Casimir effect [22]. These works show us a growing interest in the semi-classical approach of Rainbow's Gravity as to investigate quantum gravity effects through corrections to the dispersion relation of relativistic quantum fields.…”