Fermionic Dynamics in a (2+1)-Dimensional Rainbow Universe

According to the rainbow formalism of general relativity, as a particle engages with space-time through its movement, it alters the fabric of space-time, and this manifests itself in rainbow functions. Therefore, the dynamics of the particle necessitate a redefinition within the newly textured space-time. In this context, an exact solution to the Dirac equation has been investigated to determine the dynamics of Dirac particles within the (2+1)-dimensional rotating symmetric rainbow universe in the present study. So, the equation representing the energy eigenvalues of Dirac particles and the corresponding eigenfunctions in terms of the associated Laguerre polynomials have been derived. Notably, it has been observed that the energies and corresponding eigenfunctions of spin-1/2 fermions change dramatically due to rainbow functions. The energy eigenvalue equation has been reformulated within the general relativity limit of the rainbow formalism, and the energy eigenvalue equation representing massless Dirac particles has been obtained in this limit.