Ryden in her Introduction to Cosmology mentions acoustic oscillation at p. 167. From her account, it appears that the oscillation is, partly at least, an inference based on the use of the fluid equation as a model. Carroll and Ostlie in their Introduction have a more detailed discussion mostly p. 1259-1274. Weinberg in his cosmology text mentions it at p. 144. First the math seems pretty daunting. Second, from the accounts one may wonder if the idea of acoustic oscillations is an inference based on the fluid equation and current cosmological models or is based on independent observations that themselves imply acoustic oscillations. Where can one get some help with this? Is there a dimensional aspect to acoustic oscillation? Where does sqrt{3} come from?
Acoustic oscillations just mean small adiabatic (no entropy change) perturbations of a fluid at sufficiently high frequencies that they propagate as sound waves, i.e., periodic pressure variation waves.
The equations of sound propagation (acoustics) are derived from the fluid equations assuming small amplitude (then the derived equation are linear) and no viscosity (then entropy is not produced).
The origin of cosmological acoustic oscillations is the formation of structures by gravitational instability. Structures form by amplification of initial infinitesimal perturbations. As the universe grow in the first million years and just before gravitational instability starts to form bound structures the perturbations grow mildly as acoustic waves. The relic of these waves remain as a peak in the power spectrum of formed structures and the CMB fluctuations.
@ Robert Not everyone has the book. So if you could provide a image of the equation or write it down here, then may be more people will be interested to answer your question.
Also I recommend you to study Dodelson's book on Cosmology, Chapter 8. The whole book is awesome though!
I agree with Daniel. The rich structure in the anisotropy spectrum is the consequence of gravity-driven acoustic oscillations occurring before the atoms in the universe became neutral. The frozen-in phases of these sound waves imprint a dependence on the cosmological parameters, which gives CMB anisotropies their great constraining power. The underlying physics of the acoustic oscillations can be understood as follow:
In the very early phase of HOT universal soup, when the proton-electron plasma was tightly coupled to the photons due to Compton scattering, these components behaved as a single "photon-baryon fluid," with the photons providing most of the pressure and the baryons the inertia.
Perturbations in the gravitational potential, dominated by the dark matter component, were steadily evolving. They drive oscillations in the photon-baryon fluid, with photon pressure providing the restoring force. The perturbations are quite small, and so evolve linearly. That means each Fourier mode evolves independently and is described by a driven harmonic oscillator, with frequency determined by the sound speed in the fluid. Thus, there is an oscillation of the fluid density, with velocity π/2 out of phase and having a certain amplitude. In this sense, photons behave just like a fluid, which can be described with only two variables: the density p and the velocity v.
After the universe recombined the baryons and radiation decoupled, and the radiation could travel freely towards us. At that point the phases of the oscillations were frozen-in, and projected on the sky as a harmonic series of peaks. The main peak in the CMB spectrum is the mode that went through 1/4 of a period, reaching maximal compression. The even peaks are maximal under-densities, which are generally of smaller amplitude because the rebound has to fight against the baryon inertia. The troughs, which do not extend to zero power, are partially filled because they are at the velocity maxima.
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