Expansion, geometry, and gravity

Abstract

In general-relativistic cosmological models, the expansion history, matter content, andgeometry are closely intertwined. In this brief paper, we clarify the distinction between theeffects of geometry and expansion history on the luminosity distance. We show thatthe cubic correction to the Hubble law, measured recently with high-redshiftsupernovae, is the first cosmological measurement, apart from the cosmic microwavebackground, that probes directly the effects of spatial curvature. We illustratethe distinction between geometry and expansion with a toy model for which thesupernova results already indicate a curvature radius larger than the Hubble distance.