Trans-Planckian physics and signature change events in Bose gas hydrodynamics

TL;DR

This paper explores how emergent spacetime in a Bose gas model can undergo controlled signature changes between Lorentzian and Riemannian geometries, analyzing particle production and implications for analogue gravity experiments.

Contribution

It introduces a microscopic mechanism for signature change in emergent spacetime and studies its effects on particle production, connecting trans-Planckian physics with analogue gravity.

Findings

Controlled signature change between Lorentzian and Riemannian geometries demonstrated.

Particle production analyzed during finite-duration Euclidean-signature events.

Potential for amplifying cosmological particle production in condensed matter experiments.

Abstract

We present an example of emergent spacetime as the hydrodynamic limit of a more fundamental microscopic theory. The low-energy, long-wavelength limit in our model is dominated by collective variables that generate an effective Lorentzian metric. This system naturally exhibits a microscopic mechanism allowing us to perform controlled signature change between Lorentzian and Riemannian geometries. We calculate the number of particles produced from a finite-duration Euclidean-signature event, where we take the position that to a good approximation the dynamics is dominated by the evolution of the linearized perturbations, as suggested by Calzetta and Hu [Phys. Rev. A 68 (2003) 043625]. We adapt the ideas presented by Dray et al. [Gen. Rel. Grav. 23 (1991) 967], such that the field and its canonical momentum are continuous at the signature-change event. We investigate the interplay between the underlying microscopic structure and the emergent gravitational field, focussing on its impact on particle production in the ultraviolet regime. In general, this can be thought of as the combination of trans-Planckian physics and signature-change physics. Further we investigate the possibility of using the proposed signature change event as an amplifier for analogue "cosmological particle production" in condensed matter experiments.