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The temperature fluctuations of the Cosmic Microwave Background (CMB) have a sensitive dependence on the quantity of baryon asymmetry of the universe. In fact, analysis of CMB fluctuations is one of the ways of inferring the amount of baryon asymmetry. However, purely on physical grounds, how does one understand how the amount of baryon asymmetry controls the fluctuations CMB temperature?

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  • $\begingroup$ I have found a recent paper where the acoustic oscillations of the CMB can be connected to the baryon to photon ration arxiv.org/abs/1204.4186. I would have to spend some time reading it to understand its points, but it should answer your questions. $\endgroup$ – anna v Mar 14 at 19:37
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In the early universe, it is expected that baryons and anti-baryons existed. As the universe cooled, it would become impossible to create baryon/anti-baryon pairs. The remaining baryons and anti-baryons would annihilate, ultimately resulting in photons. The baryon to photon ratio after these annihilations run to completion characterises the baryon asymmetry; the excess of baryons to anti-baryons that must have existed in order for baryons to be present in the universe today.

The CMB arises about 400,000 years after the big-bang, when the universe cooled sufficiently to allow electrons to combine with protons and form a transparent atomic hydrogen gas. This occured at 3000 K and the photons emitted at that time have been redshifts by a factor of 1100, so they are mainly at microwave wavelengths.

To first order, the CMB is totally uniform and isotropic (after removing the effects of the peculiar velocity of our Galaxy with respect to the CMB). Small fluctuations in temperature of about 1 part in $10^5$ are caused by compressions and rarefactions in the gas at (and after) the epoch when the CMB was generated. Broadly, compressions heat the gas and cause a temperature rise and rarefactions the opposite. These acoustic oscillations can be thought of as an oscillator where radiation pressure acts as a spring that is being compressed by the tendency of gravitational mass to clump. The size of the oscillations is therefore dependent on the ratio of radiation pressure to the density of self-gravitating material.

At the time of the CMB formation, any dark energy is negligible compared with the matter density. The matter is in the form of baryons, which interact with the radiation field, and dark matter which does not. It is the baryon density which acts as the mass in the oscillation analogy above. If you increase the baryon density relative to the radiation pressure, which is controlled by the number of photons, then that mass gets bigger and has the effect of making the compressions in the oscillation deeper. If the compressions get deeper, the principle acoustic peaks in the CMB spatial spectrum get stronger.

Thus measurement of the amplitude of these acoustic peaks in the CMB spatial spectrum directly measures the baryon to photon ratio at the epoch of CMB creation, which in turn tells us what the baryon asymmetry was (in a uniform universe), because the number of baryons is conserved and the number of photons produced by baryon/anti-baryon annihilation is also (almost) conserved since mechanisms that absorb photons are in balance with mechanisms that create photons.

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  • $\begingroup$ Wonderfully thorough explanation! Thanks @RobJeffries $\endgroup$ – SRS Mar 15 at 12:38
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I am afraid this will not be a complete answer; also, there is a similar question on the site [How does the CMB constrain the baryon asymmetry? ].

If the universe were uniformly occupied by equal amounts of matter and antimatter, it is reasonable to imagine that the CMB spectrum would take note of the frequent annihilations. I am going to quote the following recent work on this. The crux of their argument is that "if large domains of matter and antimatter exist, then annihilations would take place at the interfaces between them. If the typical size of such a domain was small enough, then the energy released by these annihilations would result in a diffuse gamma ray background and a distortion of the cosmic microwave radiation". This paper in turn cites other, earlier work on this issue, but these date far back, so I will not cite them here.

If the universe had far separated regions dominated by matter or antimatter, so that annihilations were infrequent, this would not be as visible, so there is a question of how efficient annihilations have to be to leave its signature on the CMB. Nevertheless, in a uniform plasma, large enough antimatter density would have an imprint on CMB as this diffuse background.

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  • $\begingroup$ I found this even more recent paper arxiv.org/abs/1204.4186 where they study various ways a baryon asymmetry can be detected, and it seems it can be measured in the acoustic oscillations of the CMB. $\endgroup$ – anna v Mar 14 at 19:33
  • $\begingroup$ I have corrected my answer in the link you give $\endgroup$ – anna v Mar 14 at 19:59
  • $\begingroup$ Thanks, I have edited my answer accordingly. $\endgroup$ – NewUser Mar 14 at 21:53
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However, purely on physical grounds, how does one understand how the amount of baryon asymmetry controls the fluctuations CMB temperature?

From a cursory reading of this reference,, the fluctuations called acoustic oscillations on the CMB temperature

Imagine an overdense region of the primordial plasma. While this region of overdensity gravitationally attracts matter towards it, the heat of photon-matter interactions creates a large amount of outward pressure. These counteracting forces of gravity and pressure created oscillations, analogous to sound waves created in air by pressure differences.

In their model, they assume that if matter and antimatter densities exist in the primordial plasma , extra gamma rays due to the annihilations would change the acoustic oscillations by changing the densities locally where the annihilation takes place. They have modeled this behavior and fit a parameter for the baryon density to the data.

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