Note on the local calculation of decoherence of quantum superpositions in de Sitter spacetime

We study the decoherence effect of quantum superposition in de Sitter (dS) spacetime due to the presence of the cosmological horizon. Using the algebraic approach of quantum field theory on curved spacetime, we derive the precise expression for the expected number of entangling particles in the scalar field case. This expression establishes the relation between the decoherence and the local two-point correlation function. Specifically, we analyze the quantum superposition Gendankenexperiment performed by a local observer at the center of dS spacetime. We compute the entangling particle numbers in scalar field, electromagnetic field, and gravitational field scenarios. It is demonstrated that the quantum spatial superposition state can be decohered by emitting entangling particles into the cosmological horizon. Our setup is equivalent to an accelerating observer in 5-dimensional Minkowski spacetime. The results for the scalar and electromagnetic cases are consistent with those obtained in Ref.[1], which investigated the decoherence effect from the perspective of an accelerating observer in Minkovski spacetime. However, our result fixes the numerical prefactor of the gravitational decoherence.