Classical and Quantum Dynamics of Gyroscopic Systems and Dark Energy

TL;DR

This paper explores the classical and quantum behavior of gyroscopic systems in cosmology, revealing stability regions and resonant phenomena, and demonstrates how dark energy models can be formulated within this framework.

Contribution

It introduces a comprehensive analysis of gyroscopic systems in cosmology, identifying stability regions and linking them to dark energy models with exact equation of state w=-1.

Findings

Two stability regions identified: normal (positive Hamiltonian) and anomalous (indefinite Hamiltonian)

Resonant behavior observed in the 2-point correlation function within the anomalous region

Dark energy models with w=-1 can be realized as gyroscopic systems.

Abstract

Gyroscopic systems in classical and quantum field theory are characterized by the presence of at least two scalar degrees of freedom and by terms that mix fields and their time derivatives in the quadratic Lagrangian. In Minkowski spacetime, they naturally appear in the presence of a coupling among fields with time-dependent vacuum expectation values and fields with space-dependent vacuum expectation values, breaking spontaneously Lorentz symmetry; this is the case for a supersolid. In a cosmological background a gyroscopic system can also arise from the time dependence of non-diagonal kinetic and mass matrices. We study the classical and quantum dynamics computing the correlation functions on the vacuum state that minimizes the energy. Two regions of stability in parameter space are found: in one region, dubbed normal, the Hamiltonian is positive defined, while in the second region, dubbed anomalous, it has no definite sign. Interestingly, in the anomalous region the 2-point correlation function exhibits a resonant behaviour in a certain region of parameter space. We show that dynamical dark energy models (with exact equation of state $w=-1$) can be realised as a gyroscopic system.