When the temperature of the Universe was K at a redshift , electrons and protons combined to form neutral hydrogen, an event usually known as recombination ([Peebles, 1968,Zel'dovich et al, 1969]; see [Seager et al, 2000] for recent refinements). Before this epoch, free electrons acted as glue between the photons and the baryons through Thomson and Coulomb scattering, so the cosmological plasma was a tightly coupled photon-baryon fluid [Peebles & Yu, 1970]. The spectrum depicted in Plate 1 can be explained almost completely by analyzing the behavior of this pre-recombination fluid.
In §3.1, we start from the two basic equations of fluid mechanics and derive the salient characteristics of the anisotropy spectrum: the existence of peaks and troughs; the spacing between adjacent peaks; and the location of the first peak. These properties depend in decreasing order of importance on the initial conditions, the energy contents of the Universe before recombination and those after recombination. Ironically, the observational milestones have been reached in almost the opposite order.
Throughout the 1990's constraints on the location of the first peak steadily improved culminating with precise determinations from the TOCO [Miller et al, 1999], Boomerang, [de Bernardis et al, 2000] and Maxima-1 [Hanany et al, 2000] experiments (see Plate 1 top). In the working cosmological model it shows up right where it should be if the present energy density of the Universe is equal to the critical density, i.e. if the Universe is flat. The skeptic should note that the working cosmological model assumes a particular form for the initial conditions and energy contents of the Universe before recombination which we shall see have only recently been tested directly (with an as yet much lower level of statistical confidence) with the higher peaks.
In §3.2 we introduce the initial conditions that apparently are the source of all clumpiness in the Universe. In the context of ab initio models, the term ``initial conditions'' refers to the physical mechanism that generates the primordial small perturbations. In the working cosmological model, this mechanism is inflation and it sets the initial phase of the oscillations to be the same across all Fourier modes. Remarkably, from this one fact alone comes the prediction that there will be peaks and troughs in the amplitude of the oscillations as a function of wavenumber. Additionally the inflationary prediction of an approximately scale-invariant amplitude of the initial perturbations implies roughly scale-invariant oscillations in the power spectrum. And inflation generically predicts a flat Universe. These are all falsifiable predictions of the simplest inflationary models and they have withstood the test against observations to date.
The energy contents of the Universe before recombination all leave their distinct signatures on the oscillations as discussed in §3.3-§3.5. In particular, the cold dark matter and baryon signatures have now been seen in the data [Halverson et al, 2001,Netterfield et al, 2001,Lee et al, 2001]. The coupling between electrons and photons is not perfect, especially as one approaches the epoch of recombination. As discussed in §3.6, this imperfect coupling leads to damping in the anisotropy spectrum: very small scale inhomogeneities are smoothed out. The damping phenomenon has now been observed by the CBI experiment [Padin et al, 2001]. Importantly, fluid imperfections also generate linear polarization as covered in §3.7. Because the imperfection is minimal and appears only at small scales, the polarization generated is small and has not been detected to date.
After recombination the photons basically travel freely to us today, so the problem of translating the acoustic inhomogeneities in the photon distribution at recombination to the anisotropy spectrum today is simply one of projection. This projection depends almost completely on one number, the angular diameter distance between us and the surface of last scattering. That number depends on the energy contents of the Universe after recombination through the expansion rate. The hand waving projection argument of §3.1 is formalized in §3.8, in the process introducing the popular code used to compute anisotropies, CMBFAST. Finally, we discuss the sensitivity of the acoustic peaks to cosmological parameters in §3.9.