Non-commutative geometry as a realization of varying speed of light cosmology

TL;DR

This paper explores how space-time non-commutativity can lead to a varying speed of light in cosmology, resulting in novel thermal properties and potential observable signatures in gravitational wave spectra.

Contribution

It introduces a model where non-commutative geometry causes a temperature-dependent speed of light, with unique high-temperature photon properties and cosmological implications.

Findings

Deformed dispersion relations imply a frequency-dependent speed of light.

High-temperature photon spectrum deviates from standard Planck's law.

The model addresses horizon, flatness, and entropy problems in cosmology.

Abstract

We examine the cosmological implications of space-time non-commutativity, discovering yet another realization of the varying speed of light model. Our starting point is the well-known fact that non-commutativity leads to deformed dispersion relations, relating energy and momentum, implying a frequency dependent speed of light. A Hot Big Bang Universe therefore experiences a higher speed of light as it gets hotter. We study the statistical physics of this "deformed radiation", recovering standard results at low temperatures, but a number of novelties at high temperatures: a deformed Planck's spectrum, a temperature dependent equation of state $w=p/\rho$ (ranging from 1/3 to infinity), a new Stephan-Boltzmann law, and a new entropy relation. These new photon properties closely mimic those of phonons in crystals, hardly a surprising analogy. They combine to solve the horizon and flatness problems, explaining also the large entropy of the Universe. We also show how one would find a direct imprint of non-commutativity in the spectrum of a cosmic graviton background, should it ever be detected.