Expansion, geometry, and gravity

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