Flatness without CMB: The Entanglement of Spatial Curvature and Dark Energy Equation of State

Abstract

Abstract The cosmic spatial curvature parameter Ω k is constrained, primarily by cosmic microwave background data, to be very small. Observations of the cosmic distance ladder and the large-scale structure can provide independent checks of the cosmic flatness. Such late-universe constraints on Ω k , however, are sensitive to the assumptions of the nature of dark energy. For minimally coupled scalar-field models of dark energy, the equation of state w has nontrivial dependence on the cosmic spatial curvature Ω k . Such dependence has not been taken into account in previous studies of future observational projects. In this paper we use the w parameterization proposed by Miao & Huang, where the dependence of w on Ω k is encoded, and perform a Fisher forecast on mock data of three benchmark projects: a Wide Field InfraRed Survey Telescope–like SNe Ia survey, a Euclid-like spectroscopic redshift survey, and a Large Synoptic Survey Telescope–like photometric redshift survey. We find that the correlation between Ω k and w is primarily determined by the data rather than by the theoretical prior. We thus validate the standard approaches of treating Ω k and w as independent quantities.