Could the universe be infinite?

This pattern of fluctuations is incredibly intricate, with different average temperature differences on different angular scales. It also encodes an incredible amount of information about the Universe, including a startling fact: the curvature of space, as best as we can tell, is completely flat. If space were positively curved, like we lived on the surface of a 4D sphere, we would see these distant light rays converge. If it were negatively curved, like we lived on the surface of a 4D saddle, we would see those distant light rays diverge. Instead, distant light rays move in their original direction, and the fluctuations we have indicate perfect flatness.

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From the cosmic microwave background and the large-scale structure of the Universe (via baryon acoustic oscillations) combined, we can conclude that if the Universe is finite and loops back in on itself, it must be at least 250 times the size of the part we observe. Because we live in three dimensions, 250 times the radius means (250)3 times the volume, or more than 15 million times as much space. But, big as that is, it still isn’t infinite. A lower bound of the Universe being at least 11 trillion light years in all directions is tremendous, but it’s still finite.

There’s reason to believe it’s even bigger, though.

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