Open Quantum Cosmology: A study of two body quantum entanglement in static patch of De Sitter space

In this work, our prime objective is to study non-locality and long-range effect of two-body correlation using quantum entanglement from the various information-theoretic measure in the static patch of De Sitter space using a two-body Open Quantum System (OQS). The OQS is described by two entangled atoms which are surrounded by a thermal bath, which is modelled by a massless probe scalar field. Firstly, we partially trace over the bath field and construct the Gorini Kossakowski Sudarshan Lindblad (GSKL) master equation, which describes the time evolution of the reduced subsystem density matrix. This GSKL master equation is characterized by two components, these are-Spin chain interaction Hamiltonian and the Lindbladian. To fix the form of both of them, using Schwinger-Keldysh formalism we compute the Wightman functions for probe massless scalar field. Using this result along with the large time equilibrium behaviour we obtain the analytical solution for reduced density matrix. Further using this solution we compute Von-Neumann entropy, R$e'$nyi entropy, logarithmic negativity, entanglement of formation, concurrence and quantum discord in a static patch of De Sitter space. Finally, we have studied the violation of Bell-CHSH inequality, which is the key ingredient to study non-locality in primordial cosmology.