Curvature describes the geometry of the Universe. We know that there is curvature on a small scale due to gravitational effects, but this curvature is thought to average out on a large scale so that space can be approximated as Euclidean when describing the geometry of the Universe as a whole.
Current measurements of the curvature of the observable Universe are consistent with it being flat (0 curvature). However, it is possible that the Universe is curved and has a very small curvature (cosmic inflation would provide an explanation for why the curvature is so small).
Resolves YES if there is consensus in 2040 that the Universe has an overall curvature on a large scale, and that this curvature has been experimentally measured. Resolves NO if this has not happened. I may resolve to PROB if there is a measurement that is generally believed to be correct and show that the Universe has curvature, but has some doubt around it.
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If this were somehow observed by looking at distant phenomena like Cepheid stars, that would count right? This question isn't just about measuring curvature between two or more satellites?
@FedericoRottoli de Sitter space refers to space with positive curvature, which the Universe is not known to have. I think you are correct, though, that flat space doesn't necessarily mean Minkowski spacetime because the Universe is expanding.
Cosmologists assume that the universe at large scales has a Friedman-Lemaitre-Robertson-Walker spacetime which is equivalent to assuming homogeneity and isotropy. It allows for a time dependent scale factor and a spatial curvature constant. Minkowski is what you get if you set the spatial curvature to zero and the scale factor to a constant. This is definitely not how our universe is described! Spatial curvature equal to zero, maybe, but constant scale factor, clearly not
Personally, I would specify "spatial" every time I refer to the spatial curvature of the universe. One could argue that the universe certainly has curvature because it has space-time curvature in the form of the scale factor.
@FedericoRottoli no it isn't -- using the slicing used in cosmology (where the time coordinate is the proper time of a comoving observer from the origin to a given event), each space slice of flat Minkowski spacetime is hyperbolic (curvature parameter -1)
@ArmandodiMatteo just to clarify since the question has been corrected.
I was commenting on a previous version of the question which seemed to imply flat space ->Minkowski and I was objecting to it.