Rainbow gravity effects on quantum dynamics of scalar and oscillator fields in a topological defect cosmological space-time

In this paper, we investigate the quantum dynamics of scalar and oscillator fields in a topological defect space-time background under the influence of rainbow gravity's. The rainbow gravity's are introduced into the considered cosmological space-time geometry by replacing the temporal part $dt \to \frac{dt}{\mathcal{F}(\chi)}$ and the spatial part $dx^i \to \frac{dx^i}{\mathcal{H} (\chi)}$, where $\mathcal{F}, \mathcal{H}$ are the rainbow functions and $\chi=E/E_p$. We derived the radial equation of the Klein-Gordon equation and its oscillator equation under rainbow gravity's in topological space-time. To obtain eigenvalue of the quantum systems under investigations, we set the rainbow functions $\mathcal{F}(\chi)=1$ and $\mathcal{H}(\chi)=\sqrt{1-\beta\,\chi^p}$, where $p=1,2$. We solve the radial equations through special functions using these rainbow functions and analyze the results. In fact, it is shown that the presence of cosmological constant, the topological defect parameter $\alpha$, and the rainbow parameter $\beta$ modified the energy spectrum of scalar and oscillator fields in comparison to the results obtained in flat space.