Trans-Planckian Issue in the Milne Universe

TL;DR

This paper investigates the trans-Planckian problem in cosmology by analyzing scalar quantum fields in Milne universes, showing that conventional QFT results remain consistent across coordinate systems, challenging the necessity of trans-Planckian modifications.

Contribution

The study demonstrates that in flat Minkowski space, the energy momentum tensor remains zero in different Milne coordinate systems, questioning the need for trans-Planckian physics modifications.

Findings

Energy momentum tensor is zero in Minkowski and Milne coordinates with conventional QFT.

Trans-Planckian modifications do not alter the energy momentum tensor in these models.

Arguments extend to other low-curvature cosmological models, questioning trans-Planckian issues.

Abstract

The ``trans-Planckian'' challenge in cosmology appears when we trace the present physical wavelengths of fluctuations backwards in time. They become smaller and smaller until crossing the Planck scale where conventional QFT is challenged, so that unknown ultraviolet physics may be traced in the observable cosmological fluctuations. Usually this issue is addressed in the inflationary context, but trans-Planckian reasoning is much broader. We examine this logic in a simple example of scalar quantum field theory in the expanding and contracting Milne universes, where wavelengths of the eigenmodes are red- or blue-shifted. Trans-Planckian modifications of QFT should result in a UV-dependent VeV of the energy momentum tensor of a scalar field in the Milne universe. On the other hand, the Milne universe is another coordinate systems of flat Minkowski space-time, and the covariant energy momentum tensor should be the same (but vacuum-dependent) in different coordinates of flat space time. We explicitly demonstrate that in conventional QFT the energy momentum tensor, choosing the adiabatic vacuum, is identical to zero in Minkowski coordinates, and remains zero in the contracting Milne universe (due to non-trivial cancellations of contributions from particles which appear in the accelerating frame and from vacuum polarization there). In contrast to this, the trans-Planckian modification of the energy momentum tensor is not motivated. We provide a similar argument for the expanding Milne universe, where the energy momentum tensor in the conformal vacuum is non-zero. Similar arguments are applicable for other cosmological models where the curvature is much lower than Planckian which leads to conflicts with trans-Planckian considerations.