There are several cosmological models and ideas that deal with our universe's flatness problem, and they usually lead to topics like the Lambda-CDM model, the cosmological constant, vacuum genesis, and all the other interesting aspects of the ultimate fate of the universe.
It seems (maybe just to me) that these are all approaching (but never reaching) the same answer: namely, that the universe really is flat (i.e. Omega = 1, or k = 0), or at least we will continue to measure it as being flat, no matter how good our measurements get. We certainly have not proved that the universe is flat, but we have a lot of observations that suggest something very close to flat, at least for what we can observe.
So, is the current answer to "is the universe flat?" still "we don't know yet"?
What are some bleeding-edge research efforts that are addressing this question? Are there currently any strong movements in the scientific community to call this question one way or the other, or to declare it "unknowable"?
I'm not surprised that there's no consensus, but I have a hard time getting anyone to say "there's no consensus!", much less "there never will be a consensus".
Any help is appreciated!