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The Hubble constant is determined through obtaining the angular diameter distance to the last scattering surface. That's not a direct observable; instead it's inferred through trigonometry. We can directly measure the angular scale of the Baryon Acoustic oscillations in the CMB – it's the distance between troughs in the power spectrum. In the standard \(\Lambda\)CDM cosmological model, we also know the physical scale of the BAO feature, known as the sound horizon length.
Verde et al., WMAP: Parameter Estimation Methodology | astro-ph/0302218 |
Physics of the CMB great slides | [1504.06335] Physics of the Cosmic Microwave Background Radiation great review paper |
GitHub project: Tools for plotting CMB polarization power spectra
Spherical CMB map or 2D CMB map
Wayne Hu: graphic taking apart features in the power spectrum, slide 9 | CMB fluid approximation, slide 9+ |.
https://en.wikipedia.org/wiki/Cosmic_microwave_background (the refs, esp to Wayne Hu's work, are good)
Will the CMB ever recede outside our visibility: SE1 | SE2 | R1 | H1 |
Doug Scott's answer to CMB questions | Ned Wright | S1 |
https://www.ast.cam.ac.uk/~pettini/Intro%20Cosmology/Lecture09.pdf
Recombination was not an instantaneous process but proceeded relatively quickly nevertheless, with the fractional ionisation decreasing from X = 0.9 to X = 0.1 over a time interval ∆t ∼ 70,000 yr. With the number density of free electrons dropping rapidly, the time when photons and baryons decoupled follows soon, once the rate for Thomson scattering falls below the expansion rate H. Section 9.3, Photon Decoupling, pg 6 (These excellent notes cover the following epochs: Radiation-Matter Equality, Recombination, Photon Decoupling, Last Scattering.)
Physics of the cosmic microwave background anisotropy [1501.04288], by Martin Bucher | Anisotropy of the Cosmic Background Radiation and Cosmological Parameters, Bartelmann | Determining Cosmological Parameters from Anisotropies in the CMB |
Wayne Hu's writings: CMB, power spectrum, BAO, etc | Great graphic | BAO section | Lecture notes from introductory cosmology course: e.g., cosmic geometry |