Excerpts from 2018 Warner Prize lecture

This page gathers some pedagogical material on cosmological recombination and the cosmic microwave background (CMB), adapted from my Helen B. Warner prize lecture at the June 2019 AAS meeting. The full keynote presentation (250 MB) is available here.
• The plot on the right shows the ionization fraction as a function of time elapsed since the Big Bang. Specifically, this is the ratio of the abundance of free electrons to the total abundance of protons, both ionized and in hydrogen atoms. It starts at around 1.16 because primordial nucleosynthesis produces about 8 Helium nuclei per 100 protons, and each Helium nucleus carries two charges. The ionization fraction drops to about 1.08 around 20,000 years after the Big Bang, once Helium nuclei capture one electron, and briefly to 1 around 130,000 years after the Big Bang, once Helium fully recombines. Hydrogen gradually recombines between about 200,000 and 400,000 years after the Big Bang.
• The image on the left illustrates the propagation of photons as a function of time. At early times, photons frequently scatter with free electrons. As the Universe becomes more and more dilute and the abundance of free electrons drops, photons scatter less and less frequently, until they scatter one last time, around 400,000 years after the Big Bang. This is the ``last scattering" epoch, highlighted in grey.
• The image on the right shows the same thing as above, but now centered on an observer on Earth, today. Looking in any given direction amounts to following the path of photons back in time, until they reach the last-scattering epoch. From our point of view, it thus appears as if photons last scattered from a spherical surface centered around us, called the ``last-scattering surface". Of course any observer would also be at the center of their own last-scattering surface. The image below (credit: ESA) shows the Planck satellite scanning the sky, to unveil the CMB (as well as foreground emission from the Milky Way, showing as the big red patch in the middle).

Download this animation. • Until last scattering, photons and baryons (i.e. nuclei and electrons) are tightly coupled and form an ideal fluid with a large sound speed. Initial inhomogeneities in this fluid source acoustic oscillations, i.e. sound waves. The animation on the left illustrates how the superposition of many incoherent sound waves looks like. The oscillations go on until photons and baryons decouple at last scattering. The last ``snapshot" is what gets imprinted on the surface of last scattering, as the CMB. Below is the map of CMB temperature as measured by the Planck satellite (credit: Planck collaboration).

• The CMB temperature varies from direction to direction by a few parts in a 100,000, around the mean temperature of 2.73 K. The principal way to compress a CMB temperature map is to compute its angular power spectrum, which is, roughly speaking, the variance of temperature as a function of angular scale. This is shown on the right, where the data points from the Planck satellite are overlaid with the best-fit model, computed with the Boltzmann code CLASS. For an introduction to the rich physics of CMB anisotropies and to understand the features of this power spectrum, see for instance Wayne Hu's tutorials.
• In addition, the CMB is polarized, at the level of a few parts in a million, and as shown in the polarization map below (credit: Planck collaboration). Just like one extracts the temperature power spectrum, one can also extract the polarization power spectrum and the temperature x polarization cross-power spectrum; the latter is the covariance of temperature and polarization as a function of angular scale. These power spectra are shown on the left, and, along with the temperature power spectrum shown above, constitute the primary data extracted from CMB maps.

• CMB temperature and polarization power spectra depend sensitively on the detailed ionization history, i.e. the detailed way in which the Universe went through Helium and Hydrogen recombinations. This is illustrated in the animation below, where I add a little bump to the ionization fraction, with a constant 10% amplitude, and slide it forward in time. When the bump is added very early on, there is no noticeable effect on CMB power spectra, as photons scatter very frequently no matter what the detailed ionization fraction is. The largest effect is when the bump goes through the epoch of last scattering, to which CMB power spectra are most sensitive. When the bump is added much after last scattering, it makes less and less difference, as the Universe gets more and more dilute.

Download this animation.
This material is based upon work supported by the National Science Foundation (NSF) under Grant No. PHY-1820861.