  We explore a scenario of the general relativity determined by the framework
of the rainbow gravity with the purpose of searching for analogues of the
Aharonov-Bohm effect. By focusing on the confinement of the Dirac field and the
scalar field to a hard-wall confining potential in a modified background of the
cosmic string spacetime, we examine the effects of the rainbow gravity and the
topology of the cosmic string spacetime. Then, we compare each spectrum of
energy with the cases where the rainbow gravity is absent.
