At recombination, the only matter component which have a significant energy density amount are neutrinos, photons, baryons and Dark Matter. It is possible (and even likely) that today other species are present in the universe and play a role in modifying CMB anisotropies and/or structure formation. There are in principle three main parameters which can affect CMB anisotropies after the last scattering surface:

 Cosmological constant, which can both modidy the expansion rate of the universe and the growth rate of the perturbation.

 Curvature, which can have similar effect but with different amplitude.

 Reionization: if for some reason some astrophysical processes produce a large amount of UV radiation, it is possible that part of the atoms become ionized again. If the density of these new free electrons, it is possible that rescatter CMB photons.

Cosmological constant - Dark Energy

A growing number of observations seem to indicate that the largest contribution to the energy density of the universe is under the form of an unclustered component of negative pressure. This Dark energy may be of constant energy density (cosmological constant) or may have a more complicated dynamics, in which case it is usually named Quintessence. Regardless of the exact nature of this yet unknown component, the fact that it has negative pressure explains that its energy density decreases more slowly than that of Dark Matter and baryons. It is therefore expected that its energy density is significant since only a recent epoch and that it did not play any role at recombination.

Such a component can however affect CMB anisotropies in two ways:

 First, regardless of the physics at recombination, the angular size of the CMB anisotropies depend on the distance to the last scattering surface. This distance depends not only on the age of the universe today, but on the whole expansion history of the universe between recombination and now. With a negative pressure component the expansion can either slow down last fast than during the matter era or even accelerate. The fastest the expansion, the furthest the last scattering surface, so that adding a negative pressure component makes the angular size of the CMB anisotropies decrease. This effect is usually small for typical Dark Energy models.

 In addition, when such a component exists, the influence of gravity in the Euler equation decreses. Because of this, the unstable nature of Dark Matter perturbation is attenuated and their growth rate is smaller. In such case, the gravitational potential nolonger can remain constant but decrease with time. In this case, it is possible for CMB photons to exchange energy with time varying gravitational potentials. This so-called ISW effect can be a supplementary contribution to the CMB anisotropies. In principle, there are as many underdensities as overdensities in the early Universe. In the presence of Dark Energy, there are in principle as many potential wells that become shallower as potential hills that become lower. One therefore expects that photons can gain as much energy when crossing potential wells as they lose energy when crossing potential hills. This is true as long as the number of wells is large, but is nologr true when the average number of wells is small, which is what occurs at large scales. One therefore expects that the ISW effect arises on large scales only. Note that it is in principle possible to detect explicitely this effect by correlating CMB maps with large scale structures: large scales features of CMB maps should have some contribution from ISW effect, which should happen in region very very large scale structure are seen.

Regarding structure formation, the above argument can be translated as follows:

 In the presence of Dark Energy, the growth rate of perturbation slow down an can even become negligible. The amount of structures that can be formed is therfore dependent on the amount of Dark Energy: the more Dark Energy, the less structures.

Curvature

The effect of curvature on CMB anisotropies is essentially the same as that of Dark Energy. However, the most prominent feauture of curvature comes from geodesic deviation, a feauture specific to curvature: if one consider two non parallel light beams emited at the same place, their distance increases linearly with time in a Euclidean space. However, when considering hyperbolic universe, the distance between the two beams grows exponentially with their distance of emission.

This is because the relation between the perimeter of a circle grows exponentially with its diameter, not linearly. In other words, the space situated below a given distance is "larger" than in a Euclidean Universe. Equivalently, the geodesic deviation is smaller in the spherical universe. This has crucial consequence on CMB anisotropies as soon as the curvature radius is not too large as compared to the distance to the last scattering surface. In the case of a hyperbolic universe, geodesic deviation makes a given length at a given distance appear smaller than it would appear in a Euclidean universe.

This high sensivity of the geodesic deviation to the curvature radius makes the latter easy to constrain with the CMB as this is the most sensitive parameter to the position of the peaks.

Reionization

After recombination almost all free electrons have recombined with hydrogen and helium. It is however possible that early astrophysical object produce a sufficiently high UV flux to reionize matter. If this reionization happens sufficiently early, then the free electron density can be sufficiently high to rescatter some of the CMB photons. For typical models, only a fraction of the CMB photons are rescattered, so that most of the CMB photons still experienced their last scattering at recombination. Therefore, one expects to see the superposition of two CMB anisotropy spectra, one coming from recombination, the other from reionization. The main difference between the two is that reionization takes place much later and lasts much longer. Thus, the effect of the finite width of this new last scattering surface becomes dominant and damps all the small scales, so that the main contribution to this second spectrum arises only at large scales.

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