Abstract
We construct a non-commutative gauge theory for a charged scalar field and verify its invariance under local Poincaré and general coordinate transformations. We derive a general Klein–Gordon equation up to the second order of the non-commutativity parameter using the general modified field equation. As an application, we choose the Bianchi I universe and use the Seiberg–Witten maps to obtain the deformed non-commutative metric and study a particle production process. We show that non-commutativity plays the same role as an electric field, gravity and chemical potential.
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