Entanglement generation due to the background electric field and curvature of space-time

In Schwinger effect, quantum vacuum instability under the influence of an electric field leads to decay of vacuum into pairs of charged particles. We consider the entanglement of pair produced particles. We will show that the measure of entanglement depends on the geometry of space-time. Using the Schwinger pair production in curved space-time, dS(2) and AdS(2), we propose and demonstrate that the electric field can generate entanglement. In dS2 space-time, we study entanglement for scalar particles with zero spin in the absence and presence of a constant electric field. We show that the entanglement entropy depends on the choice of the alpha-vacua. But, for some values of the related parameters (mass, charge, scalar curvature, electric field), the entanglement entropy is independent of alpha. Also, we consider the generation of entanglement in the presence of a constant electric field for anti-de Sitter space-time. We will show that the positive (negative) curvature of space-time upgrades (degrades) the generated entanglement.