Entanglement Entropy in the $\sigma$-Model with the de Sitter Target Space

Understand

We derive the formula of the entanglement entropy between the left and right oscillating modes of the $\sigma$-model with the de Sitter target space.

• To this end, we study the theory in the \emph{cosmological gauge} in which the non-vanishing components of the metric on the two-dimensional base space are functions of the expansion parameter of the de Sitter space.
• The model is embedded in the causal north pole diamond of the Penrose diagram.
• We argue that the cosmological gauge is natural to the $\sigma$-model as it is compatible with the canonical quantization relations.