Rainbow Gravity Effects on Relativistic Quantum Oscillator Field 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 \(dt \rightarrow \frac{dt}{\mathcal {F}(\chi )}\) and the spatial part \(dx^i \rightarrow \frac{dx^i}{\mathcal {H} (\chi )}\), where \(\mathcal {F}, \mathcal {H}\) are the rainbow functions and \(0 \le \chi =|E|/E_p <1\) is the dimensionless parameter. 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.