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In the present paper, we solve the Dirac equation in the 2+1 dimensional exponentially expanding magnetized by uniform magnetic field and nonmagnetized universes, separately. Asymptotic behaviors of the solutions are determined. Using these results we discuss the current of a Dirac particle to discuss the polarization densities and the magnetization density in the context of Gordon decomposition method. In this work we also calculate the total polarization and magnetization, to investigate how the magnetic field affects the particle production. Furthermore, the electric and the magnetic dipole moments are calculated, and based on these, we have discussed the effects of the dipole moments on the charge distribution of the universe and its conductivity for both the early and the future time epoch in the presence/absence of a constant magnetic field and exponentially expanding spacetime.

One of the most interesting and important results of the formulation of the relativistic quantum mechanics in curved spacetime is the particle creation event in the expanding universe which was firstly discussed by Parker for the scalar particles and Dirac particles [

The Gordon decomposition of the Dirac currents is another useful tool for discussing the particle creation phenomena [

The outline of the work is as follows; in Section

The behavior of the electron in 2+1 dimensional curved space is represented by the covariant form of the Dirac equation [

The (2+1) dimensional de Sitter spacetime metric can be written as [

It is interesting in discussing if the universe is under influence in an external constant magnetic field in the beginning time. Therefore, an electromagnetic potential can be chosen as

The 2+1 dimensional Dirac current is written as

Now, we are going to discuss the Dirac currents and the dipole moments expressions for the exponentially expending universe. So, inserting (

To calculate the Dirac current components for the Dirac particle in the 2+1 dimensional exponentially expanding magnetized universe, we insert (

We exactly solve the Dirac equation in existence of the exponentially expanding magnetized and nonmagnetized universe and, from these solutions, derive some expressions for the Dirac current components and dipole moments. The particle creation in the exponentially expanding universe is only affected by the

No data were used to support this study.

The authors declare that there is no conflict of interests regarding the publication of this paper.

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