Creation of spin-1/2 particles by an electric field in de Sitter space

Abstract

In the present article we solve the Dirac equation in a de Sitter universe when a constant electric field is present. Using the Bogoliubov transformations, we compute the rate of spin 1/2 created particles by the electric field. We compare our results with the scalar case. We also analyze the behavior of the density of particles created in the limit H=0, when de Sitter background reduces to a flat space-time.11.10Qr, 04.62.+v, 98.80.Cq

Scalar pair production in a magnetic field in de Sitter universe

“…Our study proves that the particles will be most probably emitted perpendicular to the magnetic field direction. This conclusion shows that there are differences comparatively with the problem of pair production in electric field where the particles are emitted parallel with the electric field direction [6,7,15]. In the Minkowski limit the amplitude and probability are vanishing since in Minkowski scalar QED [37] this process is forbidden by the energy-momentum conservation.…”

“…Here we remark that the probability is proportional with the factor e −2π k , which is the same factor found in [6,7], where the problem of pair production in external fields on de Sitter geometry was studied by using a nonperturbative approach [6,7]. We must mention that a nonperturbative calculation of pair production in magnetic field on de Sitter geometry has been done in [9].…”

“…This paper proves for the first time how to solve the Dirac equation when a magnetic field is present, and these results represent the basis for the more recent studies that imply particle production in the presence of external fields [2][3][4][5][6][7][8][9] in curved backgrounds. An important result was obtained recently in [9], where the minimally coupled Klein-Gordon equation was solved in four dimensions in a de Sitter geometry.…”

“…The perturbative approach to the problem of fermions production in magnetic field on de Sitter geometry was used in [13], and the main results prove that the probability of pair production is nonvanishing only in strong gravitational fields. However for a complete picture of the problem of pair production in gravitational fields one needs to combine the nonperturbative results [2][3][4][5][6][7][8], with the perturbative treatment of this problem. This will imply as we mentioned above that the nonperturbative computations to be extended in four dimensions, since only in these cases we will have a complete picture on how the field equations with external field will look like and how these equations can be solved.…”

Creation of Dirac Particles in the Presence of a Constant Electric Field in an Anisotropic Bianchi I Universe

“…15 this result has been extended including a time dependent electric field More recently 16,17 , a quasiclassical approach has been applied to compute the rate of scalar as well as Dirac particles in the cosmological universe associated with the metric (1).…”