@ZachWeinersmith Just to clarify a couple of points

- We model spacetimes and spatial slices as manifolds, so that at small enough scales, they look like flat spacetime and space respectively

- The uniformity issue arises because we take the universe to be finite in age, so without inflation there just hasn't been enough time for antipodal points in the celestial sphere to show the same CMB temperature -- at the beginning of the universe, they would have been causally disconnected and no signal could have reached one from the other by today