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What is currently the most plausible model of the universe regarding curvature, positive, negative or flat?

(I'm sorry if the answer is already out there, but I just can't seem to find it...)

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up vote 4 down vote accepted

The primary authority on this is the WMAP project (though there are other observational cosmology projects springing up all the time). They analyze the CMB observations every two years, and the nine-year data was just published. The paper can be found here.

Basically, everyone assumes flatness because we know it is a very good approximation, because it simplifies the equations, and also because aesthetically being exactly flat is more appealing than being just close to flat. Thus most of the analysis is done assuming the curvature parameter $\Omega_k$ vanishes. Toward the middle of the paper, in Table 9, they show the results of fits that allow curvature to vary. They report $\Omega_k = -0.037^{+0.044}_{-0.042}$. When combined with results from other projects and surveys, they find $\Omega_k = -0.0027^{+0.0039}_{-0.0038}$.

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According to NASA the universe is flat to within 0.4%.

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