Dynamics of the Dirac Particle in an Anisotropic Rainbow Universe

Abstract

An alternative way of understanding physical effects in curved space time is to solve the associated particle equation such as the Dirac equation. It is a first-order relativistic wave equation and defines spin-1/2 massive particles like electrons and quarks. In this study, we solved the Dirac equation in an anisotropic rainbow universe. Subsequently, the reduced wave equation is obtained by making use of the asymptotic property of the Whittaker function. In the final stage, we calculate each component of the spin current density and then graphically evaluate their behavior according to the rainbow function. According to our results, the spin current density only depends on the z component of the momentum. In addition, the sign of both spin current densities is not changing with time. Finally, the current density amplitude in the high energy state or high scale parameter(ϵ=0.9) is rapidly decreasing faster than in ϵ=0.6 and ϵ=0.3.