The von Neumann boson-antiboson pair creation quantum entanglement entropy in noncommutative Bianchi I space-time

Abstract

Abstract The noncommutative Bianchi I curved space-time vierbeins and spin connections are derived. Moreover, a general Klein-Gordon equation up to the second order of the noncommutativity θ paramter and its solutions are presented. As an application within the quantum field theory approach using Bogoliubov transformations, the von Neumann boson-antiboson pair creation quantum entanglement entropy is studied. It is shown that its behavior is strongly dependent on the value of the noncommutativity θ parameter, k⊥ modes frequencies and the structure of the curved Bianchi I space-time. various discussions of the obtained numerical results are presented.