Using Gaussian-process reconstructions of cosmic distances and expansion rates, the authors find no statistically significant departure from flatness or from the cosmological principle in current data, and they forecast much tighter constraints from upcoming J-PAS and LIGO observations.
It is worth noticing that the first null condition is valid for z = 0, while the second null condition regards to z >0
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Non-parametric reconstructions of cosmic curvature: current constraints and forecasts
Using Gaussian-process reconstructions of cosmic distances and expansion rates, the authors find no statistically significant departure from flatness or from the cosmological principle in current data, and they forecast much tighter constraints from upcoming J-PAS and LIGO observations.