How did scientists use WMAP to determine the flatness of the universe?

[benk99nenm312]

Hey guys, I have a question which I've been researching for a while and just can't find much on. The WMAP measures the CMB from the farthest regions of space. It has provided a map of the early universe. Scientists did some work on this and found that the universe is flat to within a 2% margin of error. My question is, HOW in the world did they figure this? What did they do, how did they do to prove the universe is near flat? What measurements did they take?

Thanks in advance.

 

[nicksauce]

Hopefully someone can correct me if I'm wrong here...

Peaks in the CMB power spectrum correspond to angles on the sky (specifically, we need to know the angular size of the sound horizon of the last scattering surface). Angles on the sky correspond to the geometry of the universe. Using this, we can determine the geometry of the universe, and thus how flat it is.

 

[Chalnoth]

Well, actually, WMAP alone doesn't tell us much of anything about how flat (or not) our universe is. It's the combination of WMAP with data in the nearby universe that does that.

The basic idea here is that from WMAP we learn how matter was distributed in the early universe. In particular, there is a particular distance where you see the largest amount of variation (this is known as the "sound horizon": the distance that sound was able to travel since the end of inflation).

Using some physics, we can then relate how that distance scale should be related to the typical separation between galaxies today. So we compare how big the distance scale from galaxies today is to the same distance scale on the CMB. Once we do a little bit of geometry, we find that our universe is extremely flat, to within less than a percent (spatially, anyway: the space-time is quite curved).