Cosmological Origins and Evidence of Antimatter

Shivam Dixit, Mallya Aditi International School, [email protected]

Abstract – This paper aims to outline and analyze changes in the state of antimatter through the formation of the universe, exploring the relevant stages of cosmological history to study baryon asymmetry. Theoretical models which explain or address the observed phenomena of antimatter are explored. Finally, this paper examines ongoing experiments to understand the different properties of antimatter and how it may differ from matter.

INTRODUCTION

The theoretical and experimental discovery of antimatter was a revelation in the field of particle physics. It answered questions about the universe’s origins but raised many more, such as the question of its natural abundance throughout cosmological history.

This publication explores the astronomical origins of antimatter and the nature of its properties. It discusses the changes that occurred in the abundance of antimatter, what conditions elicit these changes, how different theoretical models address these changes, and how the knowledge of these changes through time can be used to gain a better understanding of antimatter at a fundamental level.

The modern theory of antimatter was proposed by Paul Dirac in 1928, and the first antiparticle, the antielectron, was discovered by Carl D. Anderson in 1932. A particle and its corresponding antiparticle are identical except for opposite quantum numbers (which numerically define the state and nature of particle interactions). For example, electrons have the electric charge -1 and the electron number +1, whereas positrons have the electric charge +1 and the electron number -1.

Matter and antimatter were likely equally abundant during the early stages of the universe. This means that there was a “symmetry” between matter and antimatter. Due to electric charge conservation, meaning charge can neither be created nor destroyed, one would expect matter and antimatter to be equally abundant. However, the universe is observed to have an overwhelmingly higher number of particles than antiparticles. Physicists suspect that the relative abundance of antimatter must have substantially decreased at some point during the universe’s history.

To study the interactions that may have caused the imbalance of abundances between matter and antimatter during the early stages of the universe, the Big Bang Theory must first be explored.

DISCUSSION

1 Antimatter in the Big Bang Theory

The Big Bang Theory describes the early stages of the universe’s evolution, beginning from a point of infinite temperature and density called the singularity at time t=0. At this point, it is theorized that the four fundamental forces–strong force, weak force, electromagnetic, and gravitational–were combined into one fundamental force. At t=10^-36s, the cosmological period of inflation started, where the universe expanded exponentially fast. Between t=10^-35s and 10^-30s, the universe grew orders of magnitude larger.^[1] Because of this expansion, as particle density decreases, the space between particles increases.

Due to this density change, the frequency of particle interactions changes. Particle interactions are proportional to their number density: if there are more particles in a sample volume, they are more likely to interact. Therefore, the rate of particle interaction is inversely related to the rate of universe expansion. This also means that there is a natural time scale that relates particle interactions and universe expansion. This relation changed significantly during the formation of the universe. When the rate of space expansion is equivalent to the rate of particle interactions, particles move apart before they have time to interact: This is when a species of particle decouples or “freezes out.”^[2] Particle species have a certain “relic density”, which is its density after freeze-out. Relic abundance is the present abundance of particles from the Big Bang, and therefore relic density can be extrapolated for a particular particle species (Figure 1).

At about t=6s after the Big Bang, electron-positron annihilation occurred. At this point, the temperature of particles in the universe dropped below the mass of electrons. This meant that colliding particles no longer had enough energy to create electron-positron pairs. Electrons and positrons are annihilated into photons, or particles of light. Photons react strongly with electrons in plasma and therefore freeze out relatively late.^[3] From this picture, it would seem that the relic abundance of electrons and positrons would be equal.

The antimatter evolution stage that has been the most difficult to explain is baryogenesis, or the creation of composite charged particles. Composite charged particles are subatomic particles that are made up of two or more elementary particles, like nucleons (protons and neutrons). Baryogenesis is the stage where there is believed to be an imbalance with particle-antiparticle annihilation. The asymmetry (difference between the abundances of the two-particle species) between particles and antiparticles is approximately a single proton for every 10⁹ photons, meaning that for every billion “annihilations”, one proton survived while its corresponding antiproton did not. This is called matter-antimatter asymmetry.^[1] At this stage, nucleons seem to have decoupled, but antinucleons continued annihilating.

The Standard Model alone does not explain what would cause the differential decoupling between matter and antimatter. Theoretically, there are specific conditions that allow this asymmetry to occur, also known as the Sakharov conditions.

2 The Sakharov Conditions

To construct a consistent theory of baryon-antibaryon asymmetry, one needs to satisfy the Sakharov conditions. These conditions are required for baryon asymmetry but do not explain its magnitude.

1. Baryon Number Violation

A baryon, such as a proton or a neutron, is a composite particle made of three quarks. Antibaryons are made of three antiquarks. The baryon number is the difference between the number of baryons and the number of antibaryons in a particle interaction. In a scenario or state where the universe is symmetric, the baryon number is conserved. To arrive at the observed asymmetry, a baryon number violation must occur to transition the universe from B = 0 to B ≠ 0.^[4]

2. C and CP Violation

CP symmetry is the conservation of charge conjugation and parity in particle interactions. Charge conjugation flips the particle charge in question, meaning every existing particle has a corresponding antiparticle. Parity refers to the symmetry in each particle’s wavefunction (distribution probability). If a particle interaction is CP conserving, the interaction looks the same when the direction of particle velocities is flipped and the charge is inverted.

In the case of baryon asymmetry, there is an obvious CP violation as the charge conjugation of matter overabundance should also mean antimatter overabundance, which is not observed. In the existing Standard Model, CP violation is possible in weak interactions. This is important as it proves that a CP violation can occur in the system of baryogenesis. However, the mechanism in the Standard Model falls orders of magnitude short in trying to explain baryon asymmetry to the extent observed in the universe. Extensions beyond the Standard Model are therefore put into place to account for other factors that may induce a CP violation during baryogenesis.^[5]

3. Processes out of Thermal Equilibrium

A particle’s thermal energy is intimately related to its kinetic energy, or energy of motion. Thermal equilibrium means that every collection of particles in a given system has the same average temperature, while the relative abundance remains the same. The baryon asymmetry is dependent on a process that does not occur in thermal equilibrium. This means that matter and antimatter would have to behave differently at some temperature, or that they would have to interact differently with the system at some temperature. It also means that matter would have to leave the system at a different time and temperature than antimatter did, thereby creating different abundances of matter and antimatter.^[6]

 

3. Evidence of the Baryon Asymmetry

To understand why the matter-antimatter asymmetry exists, evidence as to why matter and antimatter are not symmetric, both in theory and in observation, must be explored.

1. Observational Evidence

Matter-antimatter annihilation produces large amounts of high-energy photons which are detected easily. Sensors would detect a much larger number of photons if antimatter was in greater abundance. Any non-negligible amounts of antimatter would not have been able to survive for this long without undergoing annihilation. If there were any significant amount of antimatter, it would annihilate the matter particles of the interstellar medium. Any large celestial object made of antimatter would undergo annihilation quickly. The observed annihilations place constraints on the antimatter fraction (ratio of surviving antimatter to matter) to less than 10^-15.^[3]

2. Theoretical Argument Against a Symmetric Universe

Theoretically, one can try and account for a symmetric universe through the same means arrived at in an asymmetric one, by considering a theory for a matter-antimatter symmetric universe.

At cooler temperatures during cosmological history, the time scale of nucleon and antinucleon interaction is shorter than that of universe expansion. At one point, the abundance of nucleon-antinucleon pairs would become so little that they would practically cease to annihilate. However, the relic abundance of nucleon-antinucleon pairs predicted at this point would fall nine orders of magnitude short (a factor of 10⁹) of the observed nucleon abundance. As a result of the low density of nucleons, primordial nucleosynthesis (stage of the Big Bang during which protons and neutrons were created) would be limited, and hence, most of what would be left after the nucleon and antinucleon freeze-out are protons and electrons. Any collapsed structures, such as stars or galaxies, are unlikely to form.^[3]

Since the asymmetry between matter and antimatter is present, one can now explore the theoretical building blocks necessary to account for this phenomenon.

4. Theoretical Frameworks on Antimatter and the Baryon Asymmetry

The Standard Model

The Standard Model includes the discovered and theorized fundamental particles in the universe. Some aspects of Sakharov conditions are part of the Standard model, such as CP violation, but out of the thermal equilibrium processes. However, even with these features, the degree to which baryon asymmetry is observed is not achieved.^[3] There are some common extensions to the Standard Model that can explain aspects of observed baryon asymmetry.

The Minimal Supersymmetric Standard Model (MSSM)

The MSSM is a well-known extension of the Standard Model. In supersymmetry, every Standard Model particle has a fundamental particle, a super-partner with the same quantum numbers except for their spin, or intrinsic angular momentum. Because there are more particles through which CP violation can occur, the magnitude of CP violation increases. This results in the production of sufficient baryon asymmetry. Experiments on Electric Dipole Moment (EDM) in the Large Hadron Collider (LHC) help constrain the boundaries within which electroweak baryogenesis can occur.^[5]

Asymmetric Particle Decay

When a massive matter particle decays into two different channels with the baryon numbers B₁ and B₂, one would expect its corresponding antiparticle to decay into two different channels with the total baryon numbers -B₁ and -B₂, therefore conserving the baryon number. CPT (charge conjugation and parity) symmetry, which is a good symmetry of the Standard Model, requires that the total decay rate of a particle stays the same as its corresponding antiparticle but does not necessitate the branching ratios (ratio of the number of particles which decay through a specific decay mode to the number of those which decay through all modes) to be the same.

Assume r to be the branching ratio into the channel with the baryon number B₁, and r’ to be the branching ratio into the channel with B₂, the equation for the total baryon number of a species is as follows:

B = (B₁ – B₂) (r-r’).

Based on observation, the baryon number is a non-zero value. This equation manifests the necessity of Sakharov conditions. If CP is not violated, r = r’ and the right-hand side (RHS) would be 0. If the baryon number is not violated, B₁ = B₂ and RHS=0. If the process were not out of thermal equilibrium, the particles would assume equilibrium abundances, and the number of particles and antiparticles produced would be equal.

The main problem with this theory is that baryogenesis must occur at high temperatures. However, inflation is said to remove any pre-existing asymmetry, after which, the temperature required is usually only temporarily attainable.^[3]

Affleck-Dine Mechanism

The Affleck-Dine Mechanism is also in the context of supersymmetry (similar to that of the MSSM). It involves baryogenesis happening at an electroweak phase transition (a phase during the early universe where the electromagnetic and weak forces combine) at a temperature around 100 GeV. First-order electroweak phase transition, as in going from separate forces to combined forces, can temporarily put the system out of thermal equilibrium. Baryon production occurs at the edges of the low-temperature vacuum. However, this process requires particles and forces beyond the Standard Model.

Many more models try to explain and quantify baryogenesis and other aspects of antimatter of both lesser and greater complexity.^[4]

5. Experiments on Antimatter

Some of the leading experiments on antimatter are explored here, along with their stages of development and analysis. These experiments can deliver insight into questions on antimatter.

Antihydrogen Experiments

PS210 at CERN (the home of the LHC) was the first experiment able to produce antihydrogen atoms in an apparatus called the Low Energy Antiproton Ring (LEAR). The first step was to create antiprotons, a task done by the Antiproton Accumulator (AA). The AA fired a beam of protons into a block of metal to produce, among other secondary particles, antiprotons. These antiprotons collided with a heavy metal nucleus in LEAR to induce an electron-positron pair. In a small number of cases, the antiproton forms a bound state with the positron to create antihydrogen. Antihydrogen, however, only lasts about 40 billionths of a second before annihilating.

A few years later, a new experimental apparatus was built at CERN from the AA, called the Antiproton Decelerator, which now produces a much greater volume of antiprotons at a higher rate than the AA. ATHENA and ATRAP (Antihydrogen TRAP) succeeded in producing relatively large amounts of antihydrogen and lowering its energy to stable configurations. It was through these experiments that CERN could begin to measure the phenomenon of matter-antimatter annihilation, glimpse into the structure of an anti-atom, and compare it to hydrogen.^[7]

The ALPHA (Antihydrogen Laser Physics Apparatus) experiment is the successor to the ATHENA experiment. The main purpose of ALPHA is to compare the properties of antihydrogen to hydrogen as a means of quantifying the anomalies and symmetry between matter and antimatter.

The ALPHA apparatus consists of many smaller components which each serve different functions.^[8] Positrons and antiprotons are separately slowed and synthesized by the atom trap to produce antihydrogen, which is stored in that same trap. Superconducting magnets are used to store the antihydrogen.^[9] At this stage, plasma size, particle count, and temperature can be measured. The longest lifespan of antihydrogen observed in this experiment is over 16 minutes, which allows time to study many properties. After trapping, the apparatus can deliver antihydrogen or antiprotons to other apparatuses at the CERN complex like AEgIS (Antihydrogen Experiment: Gravity, Interferometry, Spectroscopy) and ALPHA-g.^[10]

Other Experiments and Future Endeavours

There are quite a few experiments being conducted on antimatter at CERN and other places aside from ALPHA. These experiments provide insight into the workings of phenomena in antimatter that may have occurred during the early universe. Their purpose is to exemplify theoretical arguments that have been made to explain the nature of antimatter and the causes of asymmetry.

The ASACUSA (Atomic Spectroscopy And Collisions Using Slow Antiprotons) experiment at CERN studies the fundamentals of the symmetry between matter and antimatter. It aims to measure a very precise value called the hyperfine structure, a measurement of antihydrogen’s energy configurations. It also compares properties like mass between antiprotons and protons and studies the interactions of antimatter with various kinds of matter. This varied series of interaction studies may lead to the discovery of unexpected anomalies in antimatter.^[11]

The ALPHA-g experiment is an extension of this experiment with a trapping mechanism solely devoted to measuring the gravitational acceleration of antimatter. It is designed to measure the sign and magnitude of acceleration. Current theory suggests that antimatter and matter should experience gravity the same as matter. Trapped antihydrogen at 540mK would bounce about 1000 times within 10 seconds. Different fractions of the total number of particles can be detected at the top and bottom of the bounce trajectory, whose values can be used to determine the sign of gravitational acceleration. The experiment is important to confirm whether the Standard Model theory is correct in the fact that antimatter exhibits the same gravitational behavior as matter.^[12]

BASE (Baryon Antibaryon Symmetry Experiment) is an experiment that compares the magnetic moments of protons and antiprotons. It measures properties like spin-state and oscillation in a magnetic field. It uses the measurement of the corresponding frequencies (larmor frequency and cyclotron frequency) to measure the magnetic moment with high precision. A measurable difference in these quantities could be the key to understanding the baryon asymmetry.^[12,13]

The AMS (Alpha Magnetic Spectrometer) is an experiment based on the International Space Station. It is used in the study of antimatter in cosmic rays (high-energy protons and atomic nuclei), which are useful in understanding newer cosmic phenomena. A recent analysis done on a sample of high-energy positrons concluded that they seem to have largely originated from dark matter annihilation.^[14] Experiments on newer samples may enhance scientists’ understanding of baryogenesis and its possible occurrence in the later stages of universe formation.

The GAPS (General Anti-Particle Spectrometer) experiment aims to study the nature of dark matter through the measurement of low-energy cosmic-ray antiparticles. Dark matter particles seem to make up about 84% of known matter, yet do not seem to correlate with any Standard Model particle. Dark matter hypothetically decays into Standard Model particles, including certain antimatter particles. Dark matter has not yet been observed, but the detection would have exciting implications beyond the Standard Model physics.^[15]

ELENA (Extra Low ENergy Antiproton ring) is a newer apparatus at CERN. It is a deceleration ring used to slow antiproton beams, making them easier to trap, observe, and probe. Links to all of AEGIS, ALPHA, ASACUSA, ATRAP, and BASE are due to be installed and will make experimental measurements much easier to obtain.^[16] A new experiment called the PUMA (antiProton Unstable Matter Annihilation) project is planned, involving ELENA in combination with ISOLDE, which measures the radioactive decay of atomic nuclei.^[17]

The experiments in this section not only reaffirmed basic theories but also offered new observations of antimatter that were more unexpected than others. One such example is the observation that at high energies, spontaneous conversions between matter and antimatter can occur. If more of these particles decayed into matter than into antimatter, this could be a factor in explaining the baryon asymmetry.

CONCLUSION

This paper has addressed and elucidated some of the important aspects of antimatter. It has been demonstrated how antimatter plays a crucial role in well-established theoretical frameworks (the Big Bang Theory and the Standard Model) and in new models which involve extensions or modifications to these pre-existing theories. Various experiments have been looked at, which hope to achieve different types of insights on the nature of antimatter and major differences between matter and antimatter. The various aspects of theoretical and empirical knowledge have been connected, to aid in the understanding of cosmological antimatter in a highly dense and concise manner. This paper may serve as a bridge for those who have little understanding in these subjects to begin exploring the countless aspects of cosmology and antimatter.

Major questions such as the origin of baryon asymmetry and the properties of antimatter at a quantum level could be key to understanding more about other interesting cosmic phenomena, such as the existence of dark matter. Theoretical constructs such as CP symmetry are critical in understanding many other cosmic phenomena. The successful observation of CP violation in particle-antiparticle annihilations would cement the understanding of the Sakharov conditions required for baryon asymmetry to occur.

Current observations of antimatter are possible due to the ability of experiments to slow particles to non-relativistic speeds. Experiments on antimatter that involve relativistic antiparticles may be difficult to engineer but not entirely impossible. By performing a similar series of experiments on low-energy particles as done in high-energy scenarios, physicists could see a distinction in antimatter that would otherwise be unobservable. Higher temperature also closely emulates the thermal state of the early universe, when particle annihilation is theorized to have largely occurred.

Antimatter has the potential to be practically useful in areas such as space travel. Matter-antimatter annihilation releases massive amounts of energy for the scale at which they occur. These annihilations are also 100% efficient, in the sense that all mass is converted into energy. Therefore, antimatter could be a viable source of power in reactors and thrust in transport as it is extremely energy dense. However, current technology does not produce antimatter in large enough amounts to make this feasible, but it is an active area of research.

As technical understanding of antimatter and technology improves, the potential for discoveries increases. In the near future, scientists may be able to both theoretically and empirically understand why antimatter is naturally different from matter and how it has shaped the universe’s formation.

Acknowledgments:

I would like to acknowledge the guidance of Carissa Cesarotti from Harvard University in the development of this research paper.

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FIGURE REFERENCES

Figure [1] Baumann, Daniel. Figure 3.2 in Cosmology: Chapter 3. Amsterdam University: Amsterdam Cosmology Group [graph]. https://www.dropbox.com/s/5slirav7yd9mocf/Chapter3.pdf?dl=0 (under creative commons)

Figure [2] Andresen, G.B. “The ALPHA antihydrogen trapping apparatus” [diagram]. Accessed November 3, 2020. 1104.4982.pdf (arxiv.org) (under creative commons)

About the author

Shivam Dixit is a student in Mallya Aditi International School in Bangalore. He is passionate about cosmology, astrophysics, and engineering. He has done projects and courses in CAD, computer science, computer hardware, and cosmology. He wants to make the future of air and space travel fast, efficient, and sustainable. He plans to pursue aerospace engineering in the future.