Dark energy and projective symmetry

Abstract

Nurowski [P. Nurowski, Is dark energy meaningless?, arXiv:1003.1503 [math.DG]] 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.