Charged scalar bosons in a Bonnor-Melvin-$\mathrm{\Lambda }$ universe at conical approximation

The quantum dynamics of charged scalar bosons in a Bonnor-Melvin-$\mathrm{\Lambda }$ universe is considered. In this study, the behavior of charged scalar bosons is explored within the framework of the Duffin-Kemmer-Petiau (DKP) formalism. Adopting a conical approximation ($\mathrm{\Lambda }\ll 1$), we are considered two scenarios for the vector potential: a linear and quadratic vector potentials. In particular, the effects of this background in the equation of motion, phase shift, $S$-matrix, energy spectrum and DKP spinor are analyzed and discussed.