Nonequilibrium dynamics of the $\sigma$-model modes on the de Sitter space

Understand

The two-dimensional $\sigma$-model with the de Sitter target space has a local canonical description in the north pole diamond of the Penrose diagram in the cosmological gauge.

• The left and right moving modes on the embedded base space with the topology of a cylinder are entangled among themselves and interact with the time-dependent components of the metric of the de Sitter space.
• Firstly we address the issue of the existence of the untangled oscillator representation and the description of the nonequilibrium dynamics of the untangled modes.
• We show that the untangled oscillators can be obtained from the entangled operators by applying a set of Bogoliubov transformations that satisfy a set of constraints that result from the requirement that the partial evolution generator be diagonal.