Cosmologists have been debating the shape of the universe for decades. From simple observation we know the spherical shape of Earth, stars and other celestial bodies. Although, what shape is the entire universe the galaxies are embedded in?
In cosmology, a difference is made between the observable universe and the global universe. As the name suggests, the observable universe is the portion of the universe we can see and observe. The global universe factors in the entire universe, even regions emitting light that hasn’t reached us yet, if any.
Curvature, as we discussed in Einstein’s Relativity series determines the shape of spacetime around black holes, stars, galaxies and that mass/energy can cause local curvature. The universe has only 5% of visible matter which can be proven definitively which leaves dark energy and dark matter having the other 95%. The mass of dark energy and dark matter isn’t definite so the definite effect on the curvature of the entire universe can’t be determined with 100% accuracy.
A Universe that is infinite and perfectly flat will have no curvature at all, or at least not enough curvature for it to be measured over an impossible distance. If the universe has positive curvature, the universe would be a giant hyper sphere with a boundary. If this is the case, there would possibly be an “outside” of this hypersphere.
Determining the shape of the universe asks as many questions as it answers, such as the universe having a boundary or can the Universe expansion change the shape of the universe. All topics for later posts.
Negative curvature in geometry brings an entirely different shape. Negative curvature in a shape is when the surface curves away from the tangent plane in two different directions. The most common analogy for negative curvature is that the universe is like a saddle shape or the shape between your thumb and forefinger.
All theories have plus and minus points. In the end curvature depends on mass and if a mass isn’t known, it can be difficult to define how curved this can make the universe.
GlamBlog 
You say “The mass of dark energy and dark matter isn’t definite so the definite effect on the curvature of the entire universe can’t be determined with 100% accuracy” and that “All theories have plus and minus points. In the end curvature depends on mass and if a mass isn’t known, it can be difficult to define how curved this can make the universe.” but I think you are under-estimating the precision of recent cosmological measurements. Results from the Planck satellite give values of Omega_mass = 0.315 +/- 0.018 (of which the baryonc matter is 0.0486 +/- 0.0010) and Omega_Lambda = 0.6817 +/- 0.0018 , so the proportions of mass and dark energy are very well constrained. They also show Omega_k = 0.000 +/- 0.005, so there’s very little doubt that the curvature is anything but flat.
Plenty of detail i nteh excellent OU module S383 The relativistic Universe 🙂
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Thank you for your comment. Although these masses and energy figures are from the Planck Satellite, the margin of error still exists to the point where a definite cannot be put in place as a definite figure for data purposes. I agree this is more than likely extremely close but my initial comments give a broad scope to accommodate an “introductory level” theme for my blog. I was certainly aware of it when writing but trying to simplify it would insult the good work of the satellite ☺️
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