Massless KG-oscillators in Som-Raychaudhuri cosmic string spacetime in a fine tuned rainbow gravity

Abstract

A fine tuned rainbow gravity describes both relativistic quantum particles and anti-particles alike. That is, the ratio y = E/EP in the rainbow functions g0 (y) and g1 (y) should be fine tuned into 0 <= y = E/EP <= 1 double right arrow y = |E| /E-P, otherwise rainbow gravity will only secure Planck's energy scale E-p as the maximal energy for relativistic particles and the anti-particles are left unfortunate (in the sense that their energies will be indefinitely unbounded). Using this fine tuning we discuss the rainbow gravity effect on Klein -Gordon (KG) oscillators in Som-Raychaudhuri cosmic string rainbow gravity spacetime background. We use the rainbow functions: (i) g0 (y) = 1, g1 (y) = root 1 - epsilon y(n), n = 1, 2, loop quantum gravity motivated pairs, (ii) g0 (y) = g1 (y) = (1 - epsilon y)(-1), a horizon problem motivated pair, and (iii) g0 (y) = (e(epsilon y) - 1) /epsilon y, g(1) (y) = 1, a gamma-ray bursts motivated pair. We show that the energies obtained using the first two rainbow functions in (i) completely comply with the rainbow gravity model and secure Planck's energy E-p as the maximal energy for both particles and anti-particles. The rainbow function pair in (ii) has no effect on massless KG-oscillators. Whereas, the one in (iii) does not show any eminent tendency towards the Planck's energy as the maximal energy. (c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/). Funded by SCOAP3.