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

A fine tuned rainbow gravity describes both relativistic quantum particles and anti-particles alike. That is, the ratio $y=E/{E}_{P}$ in the rainbow functions ${g}_{{}_{0}}\left(y\right)$ and ${g}_{{}_{1}}\left(y\right)$ should be fine tuned into $0\le y=E/{E}_{P}\le 1⇒y=|E|/{E}_{P}$, 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) ${g}_{{}_{0}}\left(y\right)=1$, ${g}_{{}_{1}}\left(y\right)=\sqrt{1-ϵ{y}^{n}},n=1,2$, loop quantum gravity motivated pairs, (ii) ${g}_{{}_{0}}\left(y\right)={g}_{{}_{1}}\left(y\right)={\left(1-ϵy\right)}^{-1}$, a horizon problem motivated pair, and (iii) ${g}_{{}_{0}}\left(y\right)=\left({e}^{ϵy}-1\right)/ϵy$, ${g}_{{}_{1}}\left(y\right)=1$, 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.