Double Universe

TL;DR

This paper explores the quantum properties of gravitational waves during inflation, revealing that the vacuum state is a two-mode squeezed state linked to thermal features, with non-unitary evolution described via inequivalent representations.

Contribution

It introduces a framework connecting non-unitary time evolution, squeezing, and thermal properties in inflating universes through the structure of inequivalent quantum state representations.

Findings

Vacuum state is a two-mode SU(1,1) squeezed state.

System evolution traverses unitarily inequivalent representations.

Entropy operator governs the non-unitary time evolution.

Abstract

We discuss the canonical quantization of non-unitary time evolution in inflating Universe. We consider gravitational wave modes in the FRW metrics in a de Sitter phase and show that the vacuum is a two-mode SU(1,1) squeezed state of thermo field dynamics, thus exhibiting the link between inflationary evolution and thermal properties. In particular we discuss the entropy and the free energy of the system. The state space splits into many unitarily inequivalent representations of the canonical commutation relations parametrized by time $t$ and non-unitary time evolution is described as a trajectory in the space of the representations: the system evolves in time by running over unitarily inequivalent representations. The generator of time evolution is related to the entropy operator. A central ingredient in our discussion is the doubling of the degrees of freedom which turns out to be the bridge to the unified picture of non-unitary time evolution, squeezing and thermal properties in inflating metrics.