I have just started learning GR (but have some rudimentary knowledge on differential geometry) and came across this statement: "the universe is flat with only a 0.4% margin of error".
I have read through some related stackexchange posts but I'm still not quite sure I grasp the full meaning of that statement.
1) Isn't it possible for curvature to vary from point to point? (Curvature is a local quantity, right?) So is the statement "universe is nearly flat" applicable to every single point, or is it some sort of 'global average'?
2) In GR, doesn't the presence of mass/energy alter the 4-manifold of spacetime? So I presume the 3-dimensional section of space can have a different curvature near masses such as the sun. So is the statement "universe is nearly flat" assuming the absent of any mass/energy?
