So I've read the Wikipedia articles on WMAP and CMB in an attempt to try to understand how scientists are able to deduce the curvature of the universe from the measurements of the CMB.
The Wiki article on CMB explains merely the following:
The peaks contain interesting physical signatures. The angular scale of the first peak [of the power spectrum of the cosmic microwave background radiation temperature anisotropy in terms of the angular scale] determines the curvature of the universe (but not the topology of the universe).
I don't really see, or simply do not understand, why.
I also searched Stackexchange for similar questions, like this one for example, but in that example, the marked answer simply says:
We can view the lumpiness of the Universe then by observing the cosmic microwave background radiation at high resolution.
...which doesn't really explain anything.
Can someone explain in non-mathematical or math-light terms why this data can tell us anything about the curvature of the universe?
Answer
OK, here's a brief outline that is very math light (and also somewhat oversimplified): The big idea is to compare the size of the lumpiness now to the size of the lumpiness back then when the CMB was generated, also called at the decoupling time. We measure the size of the lumpiness now by looking a galaxy superclusters and voids. We can then figure out the expansion rate of the universe, if we also measure the time and the distance back to the big bang (decoupling). From Einsteins GR we can convert the expansion rate, and also the sizes, distances and times into a curvature. (We may also assume and use some other things such as approximate uniformity, and spherical symmetry.) If you can truly explain all this, including the GR part, with a math-lite explanation, you are a much better man than I am, Charlie Brown.
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