B How to do the calculations showing the Universe is flat?

[Joshua P]

No, what we actually see now is the length of the sound horizon at decoupling after it has expanded along with the universe to the present time.

Oh. That's because of the expansion of space? The photons spread out as they move towards us?

 

[bapowell]

Yes. More generally, all length scales grow with the expansion. I understand where you're getting caught up: the horizon size at decoupling is a physically significant length scale, and we should care about this distance at that time. Indeed, we do. But, that distance, say it was a million light years, has since increased along with the expansion and so the angle it subtends today on the last scattering sphere depends on its size today.

 

[Joshua P]

@bapowell thanks, I think I get it now.

This may be the first time I don't really have a question. I'm sure I'll have one soon.

Thanks to everyone for their help.