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