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

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.

18 pages, revtex4

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• From configuration to dynamics -- Emergence of Lorentz signature in classical field theory
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• Transmission probabilities and the Miller-Good transformation
• Variational equations on mixed Riemannian-Lorentzian metrics
• Step-like discontinuities in Bose-Einstein condensates and Hawking radiation: the hydrodynamic limit
• Quantum fluctuations in trapped time-dependent Bose-Einstein condensates
• Quantum-field dynamics of expanding and contracting Bose-Einstein condensates
• Emergent spacetimes
• Signature-change events in emergent spacetimes with anisotropic scaling
• Analogue spacetimes: Toy models for "quantum gravity''