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Acoustics and Astronomy
 theory, to Hoyle’s dismay, was confirmed by Penzias’ and Wilson’s accidental 1964 discovery of the cosmic microwave background (CMB) radiation, which is the observable relic radiation from that event. The CMB also provides us with direct evidence of acoustic waves in the early universe, but it takes another entity, the “theory of inflation,” to provide a plausible mechanism for the source of the acoustic waves. (Inflationary theory is extremely solid in having many of its predictions verified, but there are still competing theories, and it is not yet a fully proven theory, so there is the teensiest bit of squishiness in this part of this story!)
The story of the acoustic waves, in very crude terms, goes like this. Just 10−37 seconds after the “instant of creation,” a field that has been dubbed the “inflaton” field, quickly de- cayed from a very symmetric, high-energy state into an asymmetric, lower energy state, creating all the matter and energy in the universe toward the end of the process. (This process of “symmetry breaking” is a familiar one in phase transitions, only here the whole universe was making a transition!) This process also expanded the universe enor- mously, much faster than the speed of light (really), merit- ing the name “inflation.” Inflation theory accounts for why space is, to a very high degree, flat (Euclidean) and solves the “horizon problem” (which is, Why are the number and size of density fluctuations the same on opposite sides of the universe, which are separated by greater distances than the speed of light times the age of the universe?). So it is, as has been mentioned, a pretty believable theory, if not yet proven. But there was also another benefit to the theory. In this the- ory, density fluctuations, which occurred due to the uncer- tainty principle of quantum mechanics, were magnified into the seeds of large-scale structure in the later universe. These seeds showed up as very slightly overdense and underdense (relative to the mean) regions of the primordial hot, expand- ing plasma containing dark matter, baryons, electrons, pho- tons, and neutrinos (Dodelson, 2003).
Considering an overdense region of the primordial plasma quickly provides a physical model for the sound waves. The overdensity region attracts matter toward it where the heat of the photon-matter interaction provides an outward force. The gravity force and the pressure force counter each other and create oscillations, very analogously to how sound in air is created by pressure differences. The speed of these acous- tic waves is relativistic, however, a bit more than half the speed of light!
Figure 4. Nine-year map of the cosmic microwave background radiation fluctuations from the Wilkinson Microwave Anisot- ropy Probe (WMAP) satellite. The basic 2.725 K blackbody spectrum has been subtracted off this picture to just show the fluctuations. Hot colors (yellow and red) indicate warmer tem- peratures; cool colors (blue) indicate colder temperatures. These translate to over- and underdense regions. Courtesy of NASA.
At about 380,000 years into the history of the universe, the expanding plasma had cooled down enough (below 3000 K) that electrons and protons could combine together into neu- tral hydrogen atoms and not be immediately dissociated by collisions. Before this, the charged matter and the photons interacted strongly via what is called Thomson scattering, and one couldn’t get very far away from the other; they were “coupled.” However, when the universe cooled enough for neutral atoms to exist, a time gloriously mislabeled as “re- combination” (as there was no previous combination!), the photons of light were free to travel their merry way with- out any significant scattering because the neutral atoms did not scatter light significantly. When this happened, the dis- tribution of the overdensity and underdensity regions (the acoustic waves) became imprinted or “frozen” on the sur- face of last scattering and thus encoded into the microwave background radiation. (It is worth noting that the photons weren’t in the microwave region then, but at higher optical frequencies; the expansion of the universe has redshifted these photons since then.)
The map of the CMB fluctuations as one looks out over the entire celestial sphere is one of mankind’s premier achieve- ments, and, as acousticians, we should be aware that we are looking at a map of the acoustic modes of oscillation of the young universe, which is probably the most important data we have to understand the universe as a whole. But what does this map tell us in particular?
One bit of acoustics it tells us is that because the intensity fluctuations are 10−4 to 10−5 smaller than the mean, the ∆p/p of the radiation pressure was of that order, which corre-
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