Which standard cosmological model is underpinned by the measured flatness of the universe?

$\Lambda$CDM model

The current leading framework for understanding the evolution and structure of the cosmos, which successfully incorporates the observed acceleration driven by dark energy ($\Lambda$) and includes cold dark matter (CDM), is the $\Lambda$CDM model. The measured flatness of the universe, constrained to within a tiny margin of error by CMB observations, is a cornerstone assumption within this standard cosmological model. The model relies on the universe possessing zero curvature ($\Omega=1$) or a curvature so slight that it is observationally indistinguishable from zero within our current horizon. This measured flatness dictates the overall spatial properties used in the equations governing cosmic evolution and structure formation within the $\Lambda$CDM paradigm.