Quantum non-linear evolution of inflationary tensor perturbations

Understand

We study the quantum mechanical evolution of the tensor perturbations during inflation with non-linear tensor interactions.

• We first obtain the Lindblad terms generated by non-linear interactions by tracing out unobservable sub-horizon modes.
• Then we calculate explicitly the reduced density matrix for the super-horizon modes, and show that the probability of maintaining the unitarity of the squeezed state decreases in time.
• The decreased probability is transferred to other elements of the reduced density matrix including off-diagonal ones, so the evolution of the reduced density matrix describes the quantum-to-classical transition of the tensor perturbations.