# How do you extract cosmological constants like $k$ or $H_0$ from the fluctuations in the CMBR (WMAP)?

I am currently reading a book about Astrophysics and also tried to find some information about it on the web, but was not able to figure it out. That is why I ask you guys now. Any help is greatly appreciated :)

I understand that the CMBR of approximately $$3\,\textrm{K}$$ has fluctuations of $$\frac{\Delta T}{T}\approx 10^{-5}$$ depending in which direction of the universe you look. I also understand that his has to be some structural information (about possible pertubations) from the last scattering surface when matter an light decoupled. However, I just don't have any idea how you are able to determine the Hubble constant and the curvature constant ($$k$$) from this. In most sources I read it was just stated that if we assume the universe is flat ($$k=0$$) than we can find the Hubble constant from WMAP data and that the WMAP data agrees well with a flat universe. I don't understand that.

I am looking for a concrete explanation how the information about $$H_0$$ and $$k$$ can be extracted from the WMAP data.

• You might find the first two links in background.uchicago.edu/index.html helpful. Also, this introductory paper is quite good (it deals with SNIA measurements rather than CMB data though): arxiv.org/abs/hep-ph/9906447v1 Finally, for a thorough and rigorous derivation have a look into the book "Physical Foundations of Cosmology" by V. Mukhanov, in particular the last chapter. Commented Mar 26, 2019 at 16:27
• You might also want to check this other question physics.stackexchange.com/questions/431780/…, the only thing you need to know is how $k$ is related to $\Omega$ which you can find in any of the links from @Photon, but the answer lies in the "shape" of the spectrum as is explained briefly in the stackExchange question. Commented Mar 29, 2019 at 13:54