Inphysical cosmology, thebaryon asymmetry problem, also known as thematter asymmetry problem or thematter–antimatter asymmetry problem,^[1][2] is the observed imbalance inbaryonic matter andantibaryonic matter in theobservable universe. As the two form and behave in nearly identical ways, it is expected that they would have been created in near equal portions by theBig Bang, where in reality matter makes up the vast majority of the universe (including the Earth and humanity). Neither thestandard model ofparticle physics nor the theory ofgeneral relativity provides a known explanation for why this should be so, and it is a natural assumption that the universe is neutral with all conservedcharges.^[3] Since this does not seem to have been the case, it is likely some physical laws must have acted differently or did not exist for matter and/or antimatter. Several competing hypotheses exist to explain the imbalance of matter and antimatter that resulted inbaryogenesis. However, there is as of yet no consensus theory to explain the phenomenon, which has been described as "one of thegreat mysteries in physics".^[4]

In 1967,Andrei Sakharov proposed^[5] a set of three necessary conditions that abaryon-generating interaction must satisfy to produce matter and antimatter at different rates. These conditions were inspired by the recent discoveries of theCosmic microwave background^[6] andCP violation in the neutralkaon system.^[7] The three necessary "Sakharov conditions" are:

• Baryon number${\displaystyle B}$ violation.
• C-symmetry andCP-symmetry violation.
• Interactions out ofthermal equilibrium.

Baryon number violation is a necessary condition to produce an excess of baryons over anti-baryons. But C-symmetry violation is also needed so that the interactions which produce more baryons than anti-baryons will not be counterbalanced by interactions which produce more anti-baryons than baryons. CP-symmetry violation is similarly required because otherwise equal numbers ofleft-handed baryons andright-handed anti-baryons would be produced, as well as equal numbers of left-handed anti-baryons and right-handed baryons. Finally, the interactions must be out of thermal equilibrium, since otherwiseCPT symmetry would assure compensation between processes increasing and decreasing the baryon number.^[8]

Currently, there is no experimental evidence of particle interactions where the conservation of baryon number is brokenperturbatively: this would appear to suggest that all observed particle reactions have equal baryon number before and after. Mathematically, thecommutator of the baryon numberquantum operator with the (perturbative)Standard Modelhamiltonian is zero:${\displaystyle [B,H]=BH-HB=0}$. However, the Standard Model is known to violate the conservation of baryon number only non-perturbatively: a global U(1) anomaly. To account for baryon violation in baryogenesis, such events (including proton decay) can occur inGrand Unification Theories (GUTs) andsupersymmetric (SUSY) models via hypothetical massive bosons such as theX boson.

The second condition for generating baryon asymmetry—violation of charge-parity symmetry—is that a process is able to happen at a different rate to its antimatter counterpart. In theStandard Model, CP violation appears as a complex phase in thequark mixing matrix of theweak interaction. There may also be a non-zero CP-violating phase in theneutrino mixing matrix, but this is currently unmeasured. The first in a series of basic physics principles to be violated was parity throughChien-Shiung Wu'sexperiment. This led to CP violation being verified in the 1964Fitch–Cronin experiment with neutralkaons, which resulted in the 1980Nobel Prize in Physics (direct CP violation, that is violation of CP symmetry in a decay process, was discovered later, in 1999). Due to CPT symmetry, violation of CP symmetry demands violation of time inversion symmetry, orT-symmetry. Despite the allowance for CP violation in the Standard Model, it is insufficient to account for the observed baryon asymmetry of the universe (BAU) given the limits on baryon number violation, meaning thatbeyond-Standard Model sources are needed.

A possible new source of CP violation was found at theLarge Hadron Collider (LHC) by theLHCb collaboration during the first three years of LHC operations (beginning March 2010). The experiment analyzed the decays of two particles, thebottom Lambda (Λ_b⁰) and its antiparticle, and compared the distributions of decay products. The data showed an asymmetry of up to 20% of CP-violation sensitive quantities, implying a breaking of CP-symmetry. This analysis will need to be confirmed by more data from subsequent runs of the LHC.^[9]

One method to search for additional CP-violation is the search forelectric dipole moments of fundamental or composed particles. The existence of electric dipole moments in equilibrium states requires violation of T-symmetry. That way finding a non zero electric dipole moment would imply the existence of T-violating interactions in the vacuum corrections to the measured particle. So far all measurements are consistent with zero putting strong bounds on the properties of the yet unknown new CP-violating interactions.

In the out-of-equilibrium decay scenario,^[10] the last condition states that the rate of a reaction which generates baryon-asymmetry must be less than the rate of expansion of the universe. In this situation the particles and their corresponding antiparticles do not achieve thermal equilibrium due to rapid expansion decreasing the occurrence of pair-annihilation.

Another possible explanation of the apparent baryon asymmetry is that matter and antimatter are essentially separated into different, widely distant regions of theuniverse. 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.^[11] Along the boundary between matter and antimatter regions, however, annihilation (and the subsequent production ofgamma 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.^[12][13] 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.^[4]

The state of the universe, as it is, does not violate theCPT symmetry, because theBig 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 flowback 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 creatingelectron–positron pairs in avacuum. This model, devised by physicists from thePerimeter Institute for Theoretical Physics inCanada, proposes that temperature fluctuations in thecosmic microwave background (CMB) are due to the quantum-mechanical nature of space-time near the Big Bang singularity.^[14] 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.^{[citation needed]}Quantum uncertainty causes the universe and antiuniverse to not be exact mirror images of each other.^[15]

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 fordark matter. Such a universe-antiuniverse pair would produce large numbers of superheavyneutrinos, also known assterile neutrinos. These neutrinos might also be the source of recently observed bursts of high-energycosmic rays.^[16]

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^[17], thus previous conditions generate a boost bias increasing the rate of matter over antimatter.

The challenges to the physics theories are then to explainhow to produce the predominance of matter over antimatter, and also themagnitude of this asymmetry. An important quantifier is theasymmetry parameter,

${\displaystyle \eta =\frac{n_B-n_{\overline{B}}}{n_{\gamma }}.}$

This quantity relates the overall number density difference between baryons and antibaryons (n_B andn_B, respectively) and the number density ofcosmic background radiationphotonsn_γ.

According to the Big Bang model, matter decoupled from thecosmic background radiation (CBR) at a temperature of roughly3000kelvin, corresponding to an average kinetic energy of3000 K / (10.08×10³ K/eV) =0.3 eV. After the decoupling, thetotal number of CBR photons remains constant. Therefore, due to space-time expansion, the photon density decreases. The photon density at equilibrium temperatureT per cubic centimeter, is given by

${\displaystyle n_{\gamma }=\frac{1}{{\pi }^2}{\left(\frac{k_{B}T}{\hslash c}\right)}^3\times {\int }_0^{\mathrm{\infty }}\frac{x^2}{e^x-1}dx=\frac{1}{{\pi }^2}{\left(\frac{k_{B}T}{\hslash c}\right)}^3\times 2\zeta (3)\approx 20.3{\left(\frac{T}{1\text{K}}\right)}^3{\text{cm}}^{-3},}$

withk_B as theBoltzmann constant,ħ as thePlanck constant divided by 2π andc as the speed of light in vacuum, andζ(3) asApéry's constant. At the current CBR photon temperature of2.725 K, this corresponds to a photon density n_γ of around 411 CBR photons per cubic centimeter.

Therefore, the asymmetry parameterη, as defined above, isnot the "good" parameter. Instead, the preferred asymmetry parameter uses theentropy densitys,

${\displaystyle {\eta }_s=\frac{n_B-n_{\overline{B}}}{s}}$

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

${\displaystyle s\stackrel{\mathrm{d}\mathrm{e}\mathrm{f}}{=}\frac{\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{p}\mathrm{y}}{\mathrm{v}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e}}=\frac{p+\rho }{T}=\frac{2{\pi }^2}{45}{g}_{\ast }(T)T^3}$

withp andρ as the pressure and density from the energy density tensorT_μν, andg_* as the effective number of degrees of freedom for "massless" particles (inasmuch asmc² ≪k_BT holds) at temperatureT,

${\displaystyle g_{\ast }(T)=\sum _{i=\mathrm{b}\mathrm{o}\mathrm{s}\mathrm{o}\mathrm{n}\mathrm{s}}{g}_i{\left(\frac{T_i}{T}\right)}^3+\frac{7}{8}\sum _{j=\mathrm{f}\mathrm{e}\mathrm{r}\mathrm{m}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}}{g}_j{\left(\frac{T_j}{T}\right)}^3,}$

for bosons and fermions withg_i andg_j degrees of freedom at temperaturesT_i andT_j respectively. Presently,s = 7.04n_γ.

• Baryogenesis
• CP violation
• List of unsolved problems in physics

• Concepts in astrophysics
• Antimatter
• Asymmetry
• Unsolved problems in physics

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