Cosmology Notes

The decoupling epoch is when the photon optical depth is one. The drag epoch is when the baryon optical depth is one. Since there are many more photons than baryons, the photons “decouple” (stop noticing the baryons) before the baryons stop noticing the photons. [source] the sound horizon at baryon decoupling, r_drag [2004.09487]

After recombination, without the pressure of the photons, the baryons simply fall into the Newtonian potential wells with the cold dark matter, an event usually referred to as the end of the Compton drag epoch. [source]

Prior to the recombination of baryons and electrons, the large density of free electrons couples the baryons to the photons through Coulomb and Compton interactions so that the three species move together as a single fluid. This continues until, in the process of recombination, the rate of Compton scattering between photons and electrons becomes too low, freeing the baryons from the photons. We thus define the drag epoch z_d as the time at which the baryons are released from the Compton drag of the photons in terms of a weighted integral over the Thomson scattering rate. [source, pg4]

The time when the baryons are “released” from the drag of the photons is known as the drag epoch, z_d. From then on photons expand freely while the acoustic waves “freeze in” the baryons in a scale given by the size of the horizon at the drag epoch. Four species: Dark matter, Baryons, Photons & Neutrinos. Initial perturbations adiabatic: all species perturbed approximately same fractional amount. Neutrinos do not interact and move too fast to be stopped by gravity, so they stream away Dark matter responds to gravity and falls onto the perturbation overdensity Perturbation dominated by photons and baryons as they are coupled. Perturbation is overdensity and overpressure. Overpressure tries to equalize with surrounding resulting in an expanding sound wave moving at the speed of sound which is approximately 2/3 the speed of light The perturbation in photons & baryons is carried outward As the expanding universe cools down, it reaches a point when the electrons and protons begin to combine Photons do not scatter as efficiently and start to decouple The sound speed drops and the pressure wave slows down Sound horizon at the drag epoch is the comoving distance a wave can travel prior to z_d The baryon acoustic oscillations provide a characteristic scale that is “frozen” in the galaxy distribution providing a standard ruler that can be measured as a function of redshift in either the galaxy correlation function or the galaxy power spectrum The BAO determination of the universe geometry is quite robust against systematics [source]

To be useful for cosmology, we need a standard ruler: an object of a known size at a single redshift, z, or a population of objects at different redshifts whose size changes in a well-known way (or is actually constant) with redshift. Ideally the standard ruler falls into both classes, which, as we will argue below, is the case for the BAO, to good approximation. [source]