# Quantum non-linear evolution of inflationary tensor perturbations

## TL;DR

This paper investigates how non-linear interactions during inflation cause tensor perturbations to transition from quantum to classical states within 5-10 e-folds, highlighting the role of reduced density matrices and Lindblad terms.

## Contribution

It provides a detailed quantum mechanical analysis of tensor perturbations' evolution, including the derivation of Lindblad terms and the quantum-to-classical transition mechanism.

## Key findings

- Quantum-to-classical transition occurs within 5-10 e-folds.
- Non-linear interactions transfer probability from unitarity to decoherence.
- Reduced density matrix evolution describes the transition process.

## Abstract

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. This is different from the classicality accomplished by the squeezed state, the suppression of the non-commutative effect, which is originated from the quadratic, linear interaction, and also maintains the unitarity. The quantum-to-classical transition occurs within 5 - 10 e-folds, faster than the curvature perturbation.