Interaction of the DKP particle with the Coulomb-type potential and Aharonov-Bohm potential under the cosmic rainbow gravity

The Duffin-Kemmer-Petiau (DKP) particle with spin 0 interacts with the Aharonov-Bohm (AB) magnetic vector potential and scalar Coulomb-type potential in the cosmic string space-times under the framework of rainbow gravity (RG). By using Bethe-Ansatz method, we obtain the energy eigenvalue and approximate solution to the wave function of the DKP particle with spin 0. We select two sets of rainbow functions and analyze their influence on the energy eigenvalue and wave functions. We find that the energy eigenvalue is determined by the parameters of the rainbow function. It further shows that the rainbow function affects the properties of the space-time where the DKP particle located, and also affects the distribution probability of DKP particles in the space.