Scalar bosons in Bonnor-Melvin-$\mathrm{\Lambda }$ universe: Exact solution, Landau levels and Coulomb-like potential

In this work, we study spin-0 particles in a spacetime whose structure is determined by a homogeneous magnetic field and a cosmological constant. For this purpose, we take into account a framework based on the Bonnor-Melvin solution with the inclusion of the cosmological constant. We write the Klein-Gordon equation, solve it, and determine the Landau levels. The effects of scalar and vector potentials are considered, and we investigate the influence of the parameters of the theory on the results, which present observable effects. The implications of the physics of a stellar model based on this framework are also discussed.