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 $d{x}^i\to \frac{d{x}^i}{\mathcal{H}(\chi )}$, where $\mathcal{F},\mathcal{H}$ are the rainbow functions and $\chi =E\mathrm{/}{E}_p$. 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.