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=== Regions of the universe where antimatter dominates === Another possible explanation of the apparent baryon asymmetry is that matter and antimatter are essentially separated into different, widely distant regions of the universe. The formation of antimatter galaxies was originally thought to explain the baryon asymmetry, as from a distance, antimatter atoms are indistinguishable from matter atoms; both produce light (photons) in the same way. Along the boundary between matter and antimatter regions, however, annihilation (and the subsequent production of gamma radiation) would be detectable, depending on its distance and the density of matter and antimatter. Such boundaries, if they exist, would likely lie in deep intergalactic space. The density of matter in intergalactic space is reasonably well established at about one atom per cubic meter. Assuming this is a typical density near a boundary, the gamma ray luminosity of the boundary interaction zone can be calculated. No such zones have been detected, but 30 years of research have placed bounds on how far they might be. On the basis of such analyses, it is now deemed unlikely that any region within the observable universe is dominated by antimatter.

=== Mirror anti-universe ===

The state of the universe, as it is, does not violate the CPT symmetry, because the Big Bang could be considered as a double sided event, both classically and quantum mechanically, consisting of a universe-antiuniverse pair. This means that this universe is the charge (C), parity (P) and time (T) image of the anti-universe. This pair emerged from the Big Bang epochs not directly into a hot, radiation-dominated era. The antiuniverse would flow back in time from the Big Bang, becoming bigger as it does so, and would be also dominated by antimatter. Its spatial properties are inverted if compared to those in our universe, a situation analogous to creating electronpositron pairs in a vacuum. This model, devised by physicists from the Perimeter Institute for Theoretical Physics in Canada, proposes that temperature fluctuations in the cosmic microwave background (CMB) are due to the quantum-mechanical nature of space-time near the Big Bang singularity. This means that a point in the future of our universe and a point in the distant past of the anti-universe would provide fixed classical points, while all possible quantum-based permutations would exist in between. Quantum uncertainty causes the universe and antiuniverse to not be exact mirror images of each other. This model has not shown if it can reproduce certain observations regarding the inflation scenario, such as explaining the uniformity of the cosmos on large scales. However, it provides a natural and straightforward explanation for dark matter. Such a universe-antiuniverse pair would produce large numbers of superheavy neutrinos, also known as sterile neutrinos. These neutrinos might also be the source of recently observed bursts of high-energy cosmic rays.

=== Cyclic cosmology === In cyclic cosmology (for example the Big Bounce) the initial baryon asymmetry is order of magnitudes smaller, because it (cyclic cosmology) is entropic and not a perfect spatiotemporal defaulting, thus previous conditions generate a boost bias increasing the rate of matter over antimatter.

== Baryon asymmetry parameter == The challenges to the physics theories are then to explain how to produce the predominance of matter over antimatter, and also the magnitude of this asymmetry. An important quantifier is the asymmetry parameter,

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{\displaystyle \eta ={\frac {n_{B}-n_{\bar {B}}}{n_{\gamma }}}.}

This quantity relates the overall number density difference between baryons and antibaryons (nB and nB, respectively) and the number density of cosmic background radiation photons nγ. According to the Big Bang model, matter decoupled from the cosmic background radiation (CBR) at a temperature of roughly 3000 kelvin, corresponding to an average kinetic energy of 3000 K / (10.08×103 K/eV) = 0.3 eV. After the decoupling, the total number of CBR photons remains constant. Therefore, due to space-time expansion, the photon density decreases. The photon density at equilibrium temperature T per cubic centimeter, is given by

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{\displaystyle n_{\gamma }={\frac {1}{\pi ^{2}}}\left({\frac {k_{B}T}{\hbar c}}\right)^{3}\times \int _{0}^{\infty }{\frac {x^{2}}{e^{x}-1}}\,dx={\frac {1}{\pi ^{2}}}\left({\frac {k_{B}T}{\hbar c}}\right)^{3}\times 2\,\zeta (3)\approx 20.3\left({\frac {T}{1{\text{K}}}}\right)^{3}{\text{cm}}^{-3},}

with kB as the Boltzmann constant, ħ as the Planck constant divided by 2π and c as the speed of light in vacuum, and ζ(3) as Apéry's constant. At the current CBR photon temperature of 2.725 K, this corresponds to a photon density nγ of around 411 CBR photons per cubic centimeter. Therefore, the asymmetry parameter η, as defined above, is not the "good" parameter. Instead, the preferred asymmetry parameter uses the entropy density s,

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{\displaystyle \eta _{s}={\frac {n_{B}-n_{\bar {B}}}{s}}}

because the entropy density of the universe remained reasonably constant throughout most of its evolution. The entropy density is

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{\displaystyle s\ {\stackrel {\mathrm {def} }{=}}\ {\frac {\mathrm {entropy} }{\mathrm {volume} }}={\frac {p+\rho }{T}}={\frac {2\pi ^{2}}{45}}g_{*}(T)T^{3}}

with p and ρ as the pressure and density from the energy density tensor Tμν, and g* as the effective number of degrees of freedom for "massless" particles (inasmuch as mc2 ≪ kBT holds) at temperature T,

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{\displaystyle g_{*}(T)=\sum _{i=\mathrm {bosons} }g_{i}\left({\frac {T_{i}}{T}}\right)^{3}+{\frac {7}{8}}\sum _{j=\mathrm {fermions} }g_{j}{\left({\frac {T_{j}}{T}}\right)}^{3},}

for bosons and fermions with gi and gj degrees of freedom at temperatures Ti and Tj respectively. Presently, s = 7.04nγ.

== See also ==

Baryogenesis CP violation List of unsolved problems in physics

== References ==