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The entanglement entropy of a free field in de Sitter space is enhanced by the squeezing of its modes. We show analytically that the expansion induces a term in the entanglement entropy that depends logarithmically on the size of the overall system, which may extend beyond the horizon. In cosmology the size of the system can be identified with the size of a spatially finite universe, or with the wavelength of the first mode that exited the horizon in the beginning of inflation.
Boutivas et al. (Wed,) studied this question.