Impact of quantum entanglement on spectrum of cosmological fluctuations

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We investigate the effect of entanglement between two causally separated open charts in de Sitter space on the spectrum of vacuum fluctuations.

• We consider a free massive scalar field, and construct the reduced density matrix by tracing out the vacuum state for one of the open charts, as recently derived by Maldacena and Pimentel.
• We formulate the mean-square vacuum fluctuations by using the reduced density matrix and show that the scale invariant spectrum of massless scalar field is realized on small scales.
• On the other hand, we find that the quantum entanglement affects the shape of the spectrum on large scales comparable to or greater than the curvature radius.