Trans-Planckian redshifts and the substance of the space-time river

TL;DR

This paper reviews how trans-Planckian redshifts relate to fundamental degrees of freedom in cosmology and black holes, discussing models, analogs, and potential laboratory tests of Hawking radiation.

Contribution

It provides a comprehensive review of models and analogs addressing trans-Planckian issues and explores future research directions in quantum gravity and laboratory observations.

Findings

Short distance cutoff may be compatible with general covariance.

Lattice models show outgoing modes via Bloch oscillations.

Condensed matter analogs could enable laboratory Hawking effect observations.

Abstract

Trans-Planckian redshifts in cosmology and outside black holes may provide windows on a hypothetical short distance cutoff on the fundamental degrees of freedom. In cosmology, such a cutoff seems to require a growing Hilbert space, but for black holes, Unruh's sonic analogy has given rise to both field theoretic and lattice models demonstrating how such a cutoff in a fixed Hilbert space might be compatible with a low energy effective quantum field theory of the Hawking effect. In the lattice case, the outgoing modes arise via a Bloch oscillation from ingoing modes. A short distance cutoff on degrees of freedom is incompatible with local Lorentz invariance, but may nevertheless be compatible with general covariance if the preferred frame is defined non-locally by the cosmological background. Pursuing these ideas in a different direction, condensed matter analogs may eventually allow for laboratory observations of the Hawking effect. This paper introduces and gives a fairly complete but brief review of the work that has been done in these areas, and tries to point the way to some future directions.