Motion of scalar particles confined in a deformed dS\(_2\) space

We mainly analyze the effective dynamics of scalar particles trapped in a two-dimensional static de Sitter (dS\(_{2}\)) spacetime from the rainbow gravity perspective. For this purpose, in the framework of gravity’s rainbow, we exactly solve the covariant Klein-Gordon equation to reach the wave function identifying relativistic dynamics of scalar particles as well as generate the corresponding energy spectrum, oscillation frequency, particle creation rate, and transmission probability, analyze them thoroughly, and highlight how the results vary depending on the selected rainbow gravity scenario. We found that the investigation implies quite amazing results. One of them is that while the General Theory of Relativity (GTR) does not give physically measurable energy values for the system we are examining, the rainbow approach of gravity allows us to obtain a real energy spectrum. Another conclusion is that if the test particles are confined to a two-dimensional geometry, the particle creation process can be observed even if the space-time model is static. The previous studies in literature indicate that the production of particles occurs in an expanding space-time or depends on the existence of a strong exterior electric field. From this point of view, our study presents a remarkable result for the creation process of relativistic scalar particles.