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I was told by a friend that a baryon acoustic oscillations are sound waves with a wavelength so large that they can travel through a vacuum. Is there any truth to this? I read what Wikipedia has to say about BAOs but I couldn't really understand the concept. Is a BAO a sound wave? Can it travel through a vacuum?

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The BAOs are indeed sound waves. Very briefly: they arise in the early Universe, driven by the competing forces of pressure and gravity. Considering a blob of gas which tries to contract due to gravity, it then feels an increase in pressure, which causes it to expand and the pressure to drop, so it then tried to collapse due to gravity, so the pressure rises, and so... this cycle is an oscillation. The wave propagates through gas (perhaps more correctly, plasma), not a vacuum. Perhaps your friend was confused by the gas being almost uniform and "featureless", but this is not equivalent to "empty space".

BAOs occur across a very large range of scales, all of which are by human standards "big". The most important scale is that corresponding to a wave which had time to complete $\frac{1}{4}$ of a cycle by the time of "recombination", which is $\sim 150\,{\rm Mpc}$ ($\sim 490\,{\rm Mly}$) in today's Universe. This scale is "visible" and a distance at which galaxies are more likely to be separated than other distances.

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  • $\begingroup$ Please could I check: are you sure that is (1/4) cycle not (1/2) cycle? $\endgroup$ Mar 14 '19 at 16:47
  • $\begingroup$ @AndrewSteane think so, from 0 amplitude to fully compressed is 1/4, and that's where you'd get a "ridge". $\endgroup$
    – Kyle Oman
    Mar 14 '19 at 21:38

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