Dark Energy and Projective Symmetry

TL;DR

This paper discusses the connection between dark energy and projective symmetry in cosmological metrics, clarifying the physical significance of projective invariance and relating it to previous research.

Contribution

It clarifies the physical relevance of projective symmetry in FLRW metrics and relates Nurowski's findings to prior work in cosmology.

Findings

Physical observables are not projectively invariant.

Nurowski's projective symmetry relates to earlier cosmological studies.

The difference in energy densities is a constant for projectively equivalent metrics.

Abstract

Nurowski [arXiv:1003.1503] has recently suggested a link between the observation of Dark Energy in cosmology and the projective equivalence of certain Friedman-Lemaitre-Robertson-Walker (FLRW) metrics. Specifically, he points out that two FLRW metrics with the same unparameterized geodesics have their energy densities differing by a constant. From this he queries whether the existence of dark energy is meaningful. We point out that physical observables in cosmology are not projectively invariant and we relate the projective symmetry uncovered by Nurowski to some previous work on projective equivalence in cosmology.