[repsilat]

>> It is that spacetime which is curved rather than just space.

> This is the crucial point that many discussions overlook

I agree completely with this (and have said as much in the past --https://www.reddit.com/r/cosmology/comments/2zy19s/bowling_b...) but

> The concept of "curvature of space" is obvious nonsense

This is emphatically not correct. Space can be curved without being embedded in a higher "meta-space". You can have a 2D surface that is curved as if it were the surface of a sphere without it actually being on an actual 3D sphere -- it just has to "connect up" the right way and have "parallel" lines bend towards each other and so on. Ditto in more dimensions.