I don't say it has to be isotropic, but observationally it looks very close to isotropic. There are quite clear signals we'd expect to see in the cosmic microwa

I don't say it has to be isotropic, but observationally it looks very close to isotropic. There are quite clear signals we'd expect to see in the cosmic microwave background if the universe was anisotropic and they aren't there: https://arxiv.org/abs/1605.07178 https://arxiv.org/abs/1605.07178 This study is (as far as I'm aware) the state of the art on this topic, and based on the CMB observations they use it appears the universe is incredibly close to isotropic. Note that because it is based on CMB data this sort of study is sensitive to what shape the universe was a long time ago when, if it is finite, it was a lot smaller.