Vacuum structure for expanding geometry

TL;DR

This paper explores the quantum structure of gravitational wave modes in an expanding de Sitter universe, revealing a complex vacuum structure linked to thermodynamics and the arrow of time.

Contribution

It demonstrates the splitting of the state space into inequivalent representations and connects the vacuum state to squeezed thermal states in expanding geometries.

Findings

State space splits into unitarily inequivalent representations.

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

Time evolution related to entropy and thermodynamic arrow.

Abstract

We consider gravitational wave modes in the FRW metrics in a de Sitter phase and show that the state space splits into many unitarily inequivalent representations of the canonical commutation relations. Non-unitary time evolution is described as a trajectory in the space of the representations. The generator of time evolution is related to the entropy operator. The thermodynamic arrow of time is shown to point in the same direction of the cosmological arrow of time. The vacuum is a two-mode SU(1,1) squeezed state of thermo field dynamics. The link between expanding geometry, squeezing and thermal properties is exhibited.