Question

There are three possibilities for the shape/curvature of the universe: positive curvature (closed), negative curvature (open), and flat curvature. These all imply different things about the ultimate fate of the expanding universe. What kinds of observable tests could cosmologists use to distinguish one curvature from the next? Please write a detailed paragraph explaining what kinds of theory/observations cosmologists would have to make to determine that the universe has negative curvature (open)?

Answer 1

How do cosmologists determine the curvature of the universe? the answer is following..

Cosmologists study the processes in the whole Universe, so occurring far enough where mankind has not penetrated before, and will not penetrate in the coming centuries.

Therefore, practical measurements of processes are impossible there, and only what comes to us can be measured – and these are photons and other particles distributed in time, direction and energy. We have no other real data. All the rest of the information we get from the alleged theories, that is, it is not the results of measurements, and the results of calculations, but because the formulas themselves have not arisen, they also are the results of theories, and require for its output a lot of assumptions, including model of space of the Universe. For example, we can't even measure the volume and mass of the Earth, but we can calculate them in a particular theory.

In different theories, the same parameters can have different values and different ratios(formulas) linking them together. For example, in models with expanding space, the lifetime of the Universe is estimated to be about 13 billion years, and in the model of the Static Universe its lifetime is infinite. Similarly, the radius of curvature in such theories can be finite in the first case, and must be infinite in the second. Even the values of the distance units "Parsec" and "light year" depend on the models.

So, all measurements in cosmology depend on the considered model of the Universe.

On the question of the topic: there was no direct measurement of the curvature of the Universe, even the dimension of the Universe space was not measured.

The paragraph regarding the negative curvature of the universe-

Negative curvature is a little trickier to visualize. The most common description is a saddle. In a negative curvature model, two lines that would be parallel on a flat plane will extend away from each other. Cosmologists call negative curvature models of the universe open universes. In these universes, there’s not enough matter to reverse or slow expansion, and so the universe continues to expand indefinitely.A universe with density greater than the critical density has positive curvature, creating a closed universe that can be imagined like the surface of a sphere. And if the universe's density is less than the critical density, then the universe is open and has negative curvature, like the surface of a saddle. Most people have a good idea of what a saddle looks like---it curves "up" in one direction and "down" in another, but no one has ever seen a uniformly negatively curved surface, for the simple reason that it cannot be constructed in three-dimensional Euclidean space! ..

Does this mean space is shaped like a flat plane, a sphere or a saddle? Not necessarily. Remember that space-time is measured in four dimensions, which reduces the usefulness of two-dimensional examples. And there are many competing theories about what the ultimate shape of the universe actually is.