  The quantum dynamics of charged scalar bosons in a Bonnor-Melvin-$\Lambda$
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 ($\Lambda\ll 1$), 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.
