Baryonic Acoustic Oscillations
Soon after the big bang, followed by inflationary epoch, the universe was in a hot plasmonic state containing a mixture of radiation and baryons. The universe being in this fluid state made it possible for the pressure waves to travel. So, the universe had baryons and environment to support acoustic oscillations.
In the CMB, we observe the anisotropies (the hot and blue spots). These temperature fluctuations are believed to be tracing the density fluctuations in the early universe. Therefore, there were fluctuations in the density across the universe after the inflationary period. These high-density regions are a mix of dark matter, baryons, photons etc (the plasma). The presence of a higher density of baryons then would attract nearby baryons through gravitational attraction. The dark matter would do the same. Therefore, the matter and radiation would collapse towards the anisotropy peaks, the centre.
However, as baryons collapse, it interacts with the photons. Two counteracting forces, therefore, act - gravity pulling inside and pressure pushing apart. The collapsing baryons increase the photonic pressure inside, which eventually leads to the formation of acoustic waves of this radiation coupled matter. Dark matter doesn't interact with electromagnetic radiation and only interacts through gravity, therefore, did not have the effect of photonic pressures and kept collapsing.
The universe was so dense at this time that the generated acoustic waves travelled nearly half the speed of light. Meanwhile, the universe kept on expanding and the temperature kept on falling. At recombination, when matter and radiation decoupled, the photons detached from the baryons and the pressure in the traversing baryonic-radiation shell collapsed. The baryons stood now nearly still as the plasmonic medium depleted (being converted to neutral atoms). Therefore, apart from the density peak at the centre, the small peak matter peak would exist at the distance where this shell stands.
Theoretically, given the speed of waves, the rate of expansion of the universe, and the density of the plasma, the distances that these shells could have travelled were calculated. It came out to be 150 MParsecs. Using the basic trigonometry, and assuming flatness of the universe, calculations reveal that it should subtend 1 degree at our end.
Now, if we take the CMB spots (red, blue spots) and see how many spots we get at different angular scales, we obtain the plot like one given below. Interestingly, data shows the peak actually at an angular scale of 1 degree. So, the randomly looking arrangement of stars actually has a pattern hidden inside.
The subsequent angular scales correspond to different harmonics. For example, the second peak corresponds to the wave which moved outwards but then came back and collapsed at the centre. In other words, other peaks are smaller ripples in this plasmonic fluid. Calculations using the ratio of first and the second peak actually reveals the amount of dark matter in the universe.
References (in short):
[1] - UCLA
[2] - ESA
[3] - KnowTheCosmos
[4] - Caltech
[5] - PBS
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