Using the CMB to verify the universe is flat

[robertjford80]

There is a video on youtube called how do we know the universe is flat. (put those keyword in youtube and you should find it, I can't post links to videos until I have 10 posts) It has something to do with using the Earth as an apex of a triangle then measuring two points on the cosmic microwave background. I'm assuming they then add the angles of the triangle up to 180 degrees. Well, how do you know what the angles of your triangle are? I've seen three tries at attempting to explain this. No one succeeds. There is also something about going around the Earth in a balloon in Antartica and I don't see why that is necessary.

 

[clamtrox]

There is a very special length scale for the perturbations in the cosmic microwave background. This scale is defined by speed of sound in the initial soup of hot plasma, and basically it's the distance across which sounds waves had time to travel before CMB decoupled from the plasma. We can determine this distance theoretically (given a certain cosmological model).

When you measure CMB today, you can see this length scale very clearly in the data: it corresponds to the highest peak in http://lambda.gsfc.nasa.gov/product...nyear/powspectra/images/med/dl7_f01_PPT_M.png. The position of the peak tells us what is the angle that this length is seen in the sky; it's about 1 square degree. We can also determine the angular diameter distance to the last scattering surface (again given a cosmological model, so the possible curvature enters the calculation here). Then we can compare to observations via
$$d_A = \frac{x}{\theta},$$
where d_A is the angular diameter distance, x is the actual size of these sound waves and $\theta$ is the angle we observe in the sky.

 

[Chronos]

Already been done, its called the baryonic acoustic oscillation of the cmb.