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When I was in school (not a physics major) I imagined universe as a 3 dimensional sphere, S3, which is a surface of a 4-dimensional ball that constantly inflates since Big Bang - hence the flow of time.

I wonder if that model can be easily disproven given what we know now?

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I imagined exactly the same. However, Planck experiments show that the universe is flat. It means, our theory was wrong - or the sphere is so big that we can't notice its curvature, thinking we're living on a flat 4-dimentional surface (almost like with Earth in ancient times)

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