# What is the curvature of the universe?

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...)

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 $\Omega_k = -0.0027^{+0.0039}_{-0.0038}$.
• This refers to flat $3$-space. On the other hand, note the answer is talking about utility of approximations. To get any nonzero negative $\Omega_k$, just take a hyperbolic manifold and inflate it until the negative curvature is however small you like it to be. Oct 18, 2020 at 12:32