Flatness without CMB - the Entanglement of Spatial Curvature and Dark Energy Equation of State

Understand

The cosmic spatial curvature parameter $\Omega_k$ is constrained, primarily by cosmic microwave background (CMB) 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 $\Omega_k$, 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 $\Omega_k$ (Miao and Huang, 2018).