Reappraisal of a model for deformed special relativity

TL;DR

This paper reevaluates an early deformed special relativity model, examining how different assumptions affect Lorentz invariance, UV dimensionality, and the spectrum of cosmological fluctuations.

Contribution

It clarifies how modifications in momentum space measure and addition rules influence the model's Lorentz invariance and fluctuation spectra.

Findings

Models preserving frame independence can achieve UV dimension 2 and scale-invariant fluctuations.

Lorentz-violating models have negative UV dimension and red spectra.

The bispectrum differs significantly between the two model variants.

Abstract

We revisit one of the earliest proposals for deformed dispersion relations in the light of recent results on dynamical dimensional reduction and production of cosmological fluctuations. Depending on the specification of the measure of integration and addition rule in momentum space the model may be completed so as to merely deform Lorentz invariance, or so as to introduce a preferred frame. Models which violate Lorentz invariance have a negative UV asymptotic dimension and a very red spectrum of quantum vacuum fluctuations. Instead, models which preserve frame independence can exhibit running to a UV dimension of 2, and a scale-invariant spectrum of fluctuations. The bispectrum of the fluctuations is another point of divergence between the two casings proposed here for the original model.