Deciphering Darkness: Implications of Empirical Evidence on Dark Matter Theories
Astrophysics Review Paper
Abstract
The immense importance yet critical lack of a conclusive theory for dark matter has made the concept a significant point of consideration in modern discussions on our understanding of the universe. Through the aid of empirical evidence, the potential theories for dark matter have been, and can be further, critically assessed to enhance the communal approach to deciphering the dark matter phenomena. This review analyses the past implications of empirical evidence from observations, detection techniques, and simulations, on leading dark matter conjectures. Implicative results discussed in this paper include the discrediting of Massively Compact Halo Objects (MACHOs) as dark matter, along with the support for Supersymmetry as an extension to the Standard Model that may enable viable dark matter candidates. With this, this paper suggests the potential future implications that further evidence may have on withstanding conjectures and finds a range of imminent developments in the field that could decisively substantiate or discredit dark matter theories.
I. Introduction
“Dark Matter” refers to a strange form of matter that defies our preconceived notions of the composition of the universe. Our understanding that the cosmos is composed of familiar baryonic matter, the protons and neutrons of our well-understood model of physics, has been immensely challenged as decades of substantial evidence point towards the majority of the matter in the universe being far more puzzling than modern science anticipated. Following historic studies and conclusions, the confrontational concept itself has become one that many modern scientists have grown to accept. Rather, the focus of scientific contention has shifted towards the potential candidates for an accurate and rigorous theory explaining dark matter, one that encapsulates the concept’s puzzling intricacies whilst being supported by empirical evidence.
This paper aims to provide eager readers an overview of the modern environment surrounding the concept of dark matter without requiring any formal prerequisite learnings in astrophysics or astronomy. This review will begin by establishing a preliminary understanding of the history of dark matter, inclusive of its first appearances within astrophysical results as well as some of the properties it has been concluded to exhibit. To follow, we will progress towards providing a brief explanation of the leading theories for dark matter, identifying a few of the intricacies pertaining to each, before discussing the prevalent methods of obtaining evidence to assess these theories. With this, the reader will be equipped to appreciate the past implications of achieved empirical evidence on dark matter theories and potential future implications with further evidence, as discussed at the end of this review.
While there exists extensive literature analysing modern developments in the field of dark matter, this paper serves as an updated review that introduces readers to the concept while covering recent findings and analysing future implications. For further reading into modern proceedings within the field of dark matter, we would recommend readers to Eugene Oks’ Brief Review of Recent Advances in Understanding Dark Matter and Dark Energy. [1] For alternative preliminary papers on dark matter, we encourage readers to explore Katherine Garrett’s Dark Matter: A Primer. [2]
II. Brief Background
Upon being coined by Fritz Zwicky in 1933, the term “Dark Matter” has been used to describe one of the most pressing discrepancies in our understanding of the universe. For millennia, the central question of “what is everything made of?” has been posed and for millennia, science has been unable to provide a definitive answer. At a point in history, the question did seem to be settled: the core constituents of our lives, our planet, the universe, were atoms. As posited by the Greek philosopher Democritus, atoms were the fundamentals of the universe, the “building blocks” of everything, and thereby received their name, coming from the Greek word for “indivisibles.”
Nearly 2500 years on from Democritus’ atomic theory, the days of assuming atoms as fundamentals are far gone and modern physics finds itself delving into the depths of the universe to truly understand the composition of everything. In our search across a universe that seems unnervingly empty and void, astronomer J.H. Oort’s findings in 1932 pointed towards a puzzling conclusion: there was far more mass than we could explain. [3] It would be uncovered that this mysterious extra mass would account for 85% of all matter, leaving our understood model of physics to be insufficient in explaining even one-sixth of the universe’s mass. [4] Oort’s findings showed that the velocities of stars calculated through Doppler shifts were significantly larger than our predictions. In fact, the stars observed by Oort were moving at speeds fast enough that they should have escaped the gravitational pull of the luminous mass they surrounded. However, these defiant stars remained in orbit.
Published just a year after Oort’s paper, Swiss astronomer Fritz Zwicky’s findings also conveyed these strange results, but on a larger scale. Zwicky studied galaxies within the Coma cluster and was able to approximate its galactic dispersion. Like Oort, he employed Doppler shifts to calculate the galaxies’ velocities and utilised the virial theorem to determine their mass. The virial theorem relates kinetic energy to potential energy through the equation:
where EK is the average kinetic energy and EGP is the average potential energy through gravitational interactions. Zwicky’s results showed that the approximate mass of a nebula within the cluster was around 9 x 1030 kilograms, or 4.5 x 1010 solar masses. Compared to previous predictions, which were based on our understanding of mass distribution in the universe, Zwicky’s calculated mass was 50 times larger. [5]
In 1983, astronomer Vera Rubin and collaborators managed to reveal a key property of this strange mass detected by Zwicky by analysing the rotation curves of dozens of galaxies. The results showed that as stars moved away from the dense galactic nucleus, their orbital velocities seemed to increase. This starkly contradicted Keplerian planetary motion laws, which determine orbital velocity to be:
where v(r) is the orbital velocity at radius r, G is the gravitational constant, and M(r) is the total mass contained within radius r. Therefore, given that the orbital velocities were sustained, or even increased, as the stars moved away from the galactic nucleus (r increased), the total mass of these stars must have also increased. [6]
It was through Rubin’s further analysis of this added mass in the NGC 3198 galaxy that a critical characteristic of the puzzling matter, also previously detected by Oort and Zwicky, was revealed. Rubin suggested that at distances closer to the galactic centre, extra luminous mass could be added to these stars, enabling them to increase orbital velocity despite r increasing. This would explain the measured velocities and result in the agreement between Keplerian predictions and observed results, as seen in Fig. 1 below. However, also seen in Fig. 1, there is an enormous discrepancy between prediction and observation past a certain point (~6 kpc).
Fig. 1: A comparison of the orbital velocities of stars within the galaxy NGC 3198 and their predicted velocities based on Keplerian laws of motion. (Source: Fig. 1 in Citation [2])
As a result, Rubin’s gathered data led to the conclusion that for stars sufficiently far away from the centre of the NGC 3198 galaxy, the added matter cannot be luminous mass sourced from the galactic nucleus; the added matter must be non-luminous; the added matter must be “dark”. Following Rubin, further observations into the far reaches of our universe have managed to establish multiple conclusions for the characteristics of dark matter, many of which have significantly devalued and substantiated certain dark matter theories. Theories that were most severely affected by these conclusions were undeniably those suggesting that dark matter was made up of large structures of ordinary baryonic matter. These objects, including brown dwarf stars and black holes, are dubbed “MACHOs”, or MAssive Compact Halo Objects.
However, significant evidential support for MACHOs was never obtained, as signs of these objects being the cause of matter fluctuations in the observed systems were absent. Therefore, as dark matter properties opposing the characteristics of MACHOs continued to be asserted through empirical evidence, the theory was largely relegated. Two critical examples of properties that devalued MACHOs as dark matter candidates were the electrically neutral and non-relativistic, or “cold”, characteristics of dark matter, two conditions that MACHOs inherently failed to exhibit. [7, 8] Though the procedure for arriving at these conclusions will not be elaborated upon in this section, Section V. 1. A. will discuss these findings in more detail.
With increased opposition, theories positing MACHOs as dark matter have been widely replaced by the conjecture that the cold, non-relativistic, dark matter is composed of Weakly Interacting Massive Particles, or WIMPs. These particles aim to satisfy the characteristics of dark matter on a far smaller scale than the large objects described in MACHO theories. With the potential validity that a WIMP theory may have in describing dark matter, the last few decades have seen the rise of a myriad of conjectures that propose certain WIMPs in apparent agreement with empirical evidence and as candidates for dark matter.
III. Leading Theories
1. Candidates from the Standard Model
The Standard Model of particle physics (SM) is an established theory developed in the 1970s aimed towards describing the fundamental particles and their corresponding interactions that govern the universe. The SM divides all known matter into two distinct groups consisting of six particles each: the quarks and the leptons. Furthermore, as seen in Fig. 2, the SM also successfully describes interactions between these particles by identifying the force-carrying particles as another group known as “gluons”. [9] A strong indicator of the SM’s success as a scientific theory is the recent finding from the Large Hadron Collider (LHC) at CERN which obtained substantial evidence indicating the presence of the Higgs Boson, a gluon that the SM itself had previously predicted. [10]
Fig. 2: A graphic depicting the categorisation of the fundamental particles, matter and force-carrying, within the Standard Model, inclusive of the Higgs Boson which was predicted by the SM and successfully detected in 2012 by the LHC. (Source: Fig. 1 in Citation [9])
In reference to dark matter, the SM realistically only offers one potential candidate that exhibits some of the necessary properties: the neutrino. Neutrinos, depicted as the grey leptons in Fig. 2, come in three generations: electron neutrinos, muon neutrinos, and tau neutrinos. [10] Neutrinos are the only stable and weakly-interacting particles proposed by the SM and as a result, they could possibly be candidates to explain dark matter. The viability of neutrinos as dark matter has been both supported and devalued through evidencing techniques, aimed at detecting neutrinos themselves as well as uncovering more characteristics of dark matter to further analyse their suitability as candidates (these techniques and their implicative results will be discussed in Section V. 1.).
Despite its success and title as “the most successful theory ever”, the SM has severe limitations in comprehensively describing the universe at a fundamental level. [11] Although the SM manages to successfully incorporate three of the four known fundamental forces, including the weak force, the strong force, and the electromagnetic force, it is unable to describe the fourth force of gravity. Along with this, the SM fails in describing other strange features of particle physics, such as the reasoning behind the large energy gap in the lowest and second-lowest observed energy states (Planck and electroweak), or why the mass of the Higgs boson is so much lower than the SM predicts, or at which energy level are the three forces in the SM unified. [10] These unanswered mysteries are known as the hierarchy problem, the fine-tuning problem, and the grand unification problem respectively.
Another limitation of the SM is its inability to explain the observed asymmetry between matter and antimatter. To elaborate, matter is far more prevalent in our universe than antimatter despite our established Charge Parity (CP) symmetry dictating that the laws of physics should be same if a particle is replaced by its antiparticle. [12] Given that the CP symmetry is not preserved in certain phenomena, which results in the well-known CP violation problem that the SM cannot explain, the success of the SM theory is significantly constrained. The CP problem will appear below as we discuss Exotic Candidates for dark matter (Section III. 3. A). However, more significantly, in Section V of this paper, the CP violation problem and its potential solution will be particularly relevant in determining the applicability of the neutrino as dark matter by suggesting the existence of the “sterile neutrino”, a particle not predicted by the SM.
2. Candidates from Supersymmetry
Supersymmetry (SUSY) is a proposed extension to the SM that, if implemented, will be able to offer effective candidates for dark matter. SUSY is best described as an additional symmetry between bosons and fermions. Fermions include protons, neutrons, electrons, and neutrinos, all of which have an integer “spin” value, a quantum property, while bosons have half-integer spins. The symmetry between these two particle types is suggested by SUSY by avoiding certain limitations through theoretical means. [13]
To elaborate, the limitation in the SM that prevents this fermion-boson symmetry from existing is the Coleman-Mandula theorem. In short, the theorem asserts that only two symmetries can exist in a quantum field theory (QFT) like the SM, and neither of these symmetries can be between fermions and bosons. [14] Through certain generalisations and lack of restrictions, SUSY manages to escape the limitations of the Coleman-Mandula theorem to suggest the existence of “superpartners”. This proposes that a certain fermion would be associated with a corresponding superpartner boson, and a certain boson would be associated with a corresponding superpartner fermion.
There are multiple reasons outside of the dark matter concept that illustrate why SUSY seems extremely appealing as an extension to the SM. Firstly, SUSY manages to solve the aforementioned hierarchy, fine-tuning, and grand unification problems faced by the SM. In relation to the hierarchy problem, SUSY has been simulated to show that it occurs in the energy gap between the Planck and electroweak scales, thus explaining the current void of activity we see at those low energy levels. In relation to the fine-tuning problem, SUSY effectively doubles the number of matter particles within the SM, as it proposes a superpartner for each boson and fermion. This solves the problem of the Higgs boson mass as each corresponding fermion and superpartner boson (or vice versa) would cancel each other out, neatly leaving a small Higgs boson mass, as detected through the LHC experiments. In relation to the grand unification problem, in a SUSY model, the three forces are actually observed to unify at a distinct energy level, something that is not seen in the SM, as depicted in Fig. 3. [14, 15]
Fig. 3: A graph that showcases how Supersymmetry solves the hierarchy problem, by occurring at energy levels between the Planck and electroweak scales, and the grand unification problem, by unifying the three forces at a distinct energy level. (Source: Fig. 3 in Citation [15])
Finally, SUSY also suggests a viable candidate for dark matter. It allows for the existence of a variety of electrically neutral and stable particles, such as the sneutrino, the superpartner to the neutrino, the graviton, superparter to the graviton (given that a quantum theory of gravity is developed), and the neutralino, a “mixture” of the neutral Higgs boson, photon, and Z boson superpartners. However, sneutrinos would annihilate too rapidly to form stable dark matter and would not appear in great enough densities to be cosmologically significant. [16] Also, gravitinos would be relativistic, meaning that they travel at or around the speed of light, and would be “hot” dark matter, clashing with dark matter’s established characteristics (increased evidence in support for dark matter being “cold” and non-relativistic will be further discussed in Section V as it has major implications on the validity of other theories). [17]
This leaves the neutralino as the most feasible candidate for dark matter that Supersymmetry posits. In fact, as we will discuss later, neutralinos are currently one of the leading WIMP candidates for dark matter, with other particle candidates from our established SM being discovered to have severe limitations in light of empirical evidence exploring dark matter properties.
3. Exotic Candidates
A. Axions
To understand where the “axion” appears from, how it is a viable dark matter candidate, and why it is commonly categorised as an “exotic” candidate, we must delve into its derivation. The axion arises from a solution to the CP-problem seen in the Quantum Chromodynamics (QCD) Lagrangian. Recall that the CP violation problem is the asymmetry between matter and antimatter in the universe in spite of physical laws necessitating symmetry between them. The QCD Lagrangian is a mathematical expression that describes the key interactions between quarks and gluons but the expression itself contains a term that can violate the CP symmetry and result in the CP problem. This violating term is the theta term (𝜭) in the Lagrangian that can result in an arbitrarily large electric dipole moment (EDM) within neutrons. Given that this large EDM has never been observed through experimentation, this arbitrary 𝜭 is a key problem. [18]
A solution to this problem comes from the model proposed by Roberto Peccei and Helen Quinn which introduces the Peccei-Quinn symmetry, a way to explain why the 𝜭 observed through experiments is never as large as that allowed by the QCD Lagrangian. Furthermore, Peccei and Quinn postulate that this symmetry is actually partially broken, leading to the appearance of a very light, scalar particle: the axion. [19] The axion is potentially a suitable candidate for dark matter as, despite its low mass, which can often result in insufficient density as seen in the case of the gravitino, axions would be so numerous across the universe that their density would make them cosmologically significant.
B. Kaluza-Klein Particles
The Kaluza-Klein model was introduced by Theodor Kaluza and Oscar Klein in the 1920s. The model was derived by applying Einstein’s theory of general relativity to five spatial dimensions and managing to retain four-dimensional gravity with Maxwell’s laws. Klein proposed that the fifth dimension that they were unable to incorporate was unobservable because it was compactified to a radius 1036 times smaller than a millimetre (-1036 millimetres). [20] To gain a perspective of how astronomically small this dimension is, the radius of an atom is approximately 1036 times smaller than the radius of the observable universe. [21]
Given these proposed infinitesimal dimensions do exist, the particles that propagate through them could be viable candidates for dark matter. More precisely, if a possible discrete symmetry known as the Kaluza-Klein parity is allowed, then the Lightest Kaluza-Klein Particle (LKP) within the pairings of the parity can be stable and act as dark matter. [22]
IV. Methods for Obtaining Empirical Evidence
1. Observations
Garnering empirical evidence through observations has long been an essential method in comprehending our known universe. By analysing the collected data from astrophysical sources, from spiral galaxies to the cosmic microwave background, certain conclusions on the characteristics of the universe and its laws can be drawn. [23] In reference to the quest for the understanding of dark matter, observational evidence can, and has, played a key role in assessing the validity of theoretical models and theories.
A particular example of implicative results from direct observation is the evidence obtained from the Bullet cluster, a collision site between two other cluster galaxies, that provided some of the most substantial proof of dark matter in our universe whilst also significantly devaluing baryonic matter theories. [24] The implications of the Bullet cluster evidence, particularly on the MACHO-based theories and our understanding of dark matter characteristics, will be discussed later in Section V. 1. A..
One of, if not the most, significant astrophysical observations has been the detection and understanding of the Cosmic Microwave Background (CMB), an excess universal temperature of 2.73 K. This temperature has been concluded to be the result of photons being released and scattering through the universe once it had cooled enough to become transparent to electromagnetic radiation (estimated to be around 380,000 years after the Big Bang). [25] Multiple space telescopes have been developed and successfully launched to further obtain data on the CMB, most notably including the COsmic Background Explorer (COBE) and the Wilkinson Microwave Anisotropy Probe (WMAP). Findings from the likes of these space telescopes have significantly developed our understanding of the universe on a larger scale and thereby our understanding of dark matter. [2]
2. Detection
Detection in astrophysics involves the identification and study of phenomena or particles that would normally be undetectable with traditional telescopes. This includes both direct and indirect detection methods to capture particle and wave emissions from universal processes. [26] These detection methods are critical in our exploration of dark matter as they aid in the search for viable particles while also strengthening our understanding of their properties and interactions.
A. Direct Detection
Direct detection of dark matter is a method of obtaining empirical evidence that concentrates on detecting dark matter particles as they interact with ordinary matter. Direct detection experiments are designed to observe these interactions and detect for certain indications, such as the scattering of nuclei or the conversion to detectable photons. As compared to indirect detection, which focuses on the byproducts of these interactions, the aim for direct detection methods is substantially more ambitious as it centres around measuring the direct presence and effects of dark matter particles, which, as established prior, are extremely weakly interacting. Nevertheless, there exists a range of direct detection methods that have been developed to aid in our search for dark matter.
One of these methods, focusing on the search for WIMP dark matter, includes the usage of a sensitive device that contains a large amount of a certain element and is able to finely detect the very small motions and interactions of the atoms within it. The main principle behind these detectors is that if WIMP dark matter is present everywhere in our universe, then it should be flowing through the detectors at all times. Despite its weak-interactions, dark matter should occasionally disrupt the atoms within the detector through collisions, resulting in a small emission of energy which can be detected. [27] The magnitude of this energy emitted can be approximated through the formula for kinetic energy:
where EK is the kinetic energy, m is the estimated mass of the WIMP (~100 GeV or 1.78 x 10-25 kg), and v is the velocity of the particle (~220 km/s). This gives us an approximation of 26.9 keV of energy that will be deposited by a WIMP if it were to interact with the detector. [2]
Given that radioactivity commonly emits energy in the MeV scales, these detector systems have to be “clean” and shielded as discrepancies due to radioactive processes would make the WIMPs impossible to detect. Further, these detectors have an “anti-coincidence veto system”, which ensures that if the primary detector within the system is set off simultaneously with the surrounding veto detectors, then the detected particle is likely a background particle, such as cosmic rays or muons, rather than a dark matter WIMP. Hence, the system rejects, or vetos, these detections to increase overall accuracy. [28]
Leading examples of direct detection experiments employing this approach include the UK Dark Matter Collaboration’s ZonEd Proportional scintillation in LIquid Noble gases (ZEPLIN-I) in the Boulby Mine, the XENON10 at the Gran Sasso Underground Laboratory, and, Cryogenic Dark Matter Search (CDMS) in the Soudan Mine. [27, 28, 29]
Though direct detection in the search for dark matter is heavily focused on detecting WIMP candidates, there exist direct detection methods aimed at detecting the exotic axions. These experiments, known succinctly as Axion Dark Matter eXperiments (ADMXs) utilise and detect the conversion of axions into photons given particular conditions. ADMXs involve the placement of a resonant microwave cavity within a strong magnetic field, which causes the axions, if present, to have their energies converted into photon frequencies. To align with the theoretical predictions of axion theories, the cavity is precisely adjusted to resonate at the frequency that corresponds with the predicted mass of an axion. [30]
Following the photonic conversion, sensitive microwave detectors and amplifiers, seen in Fig. 4, are able to detect and amplify the weak signal generated from the conversion. This amplified signal is then processed and the data is analysed to search for extra power at any frequencies, which would indicate the presence of axions and their photonic conversions. [30]
Fig. 4: A diagram depicting the main components and functions of an Axion Dark Matter Experiment detector, inclusive of the mentioned amplifiers and detectors within the microwave cavity. (Source: Fig. 2 in Citation [30])
B. Indirect Detection
Indirect detection for dark matter focuses on detecting the byproducts of interactions between potential dark matter particles, specifically secondary products rather than the dark matter particles themselves. These products can provide evidence of dark matter without the WIMPs themselves having to interact with the detector. Indirect detection in this form is particularly effective in assessing SUSY theories as SUSY particles are classed as Majorana particles, meaning that they are their own antiparticles and their annihilations emit various products that we can accurately detect. This method of obtaining empirical evidence largely concentrates on the WIMP-WIMP interactions and the emissions produced, including gamma rays, neutrinos, and antimatter. [2]
Gamma rays from WIMP annihilations are the result of quarks and antiquarks produced from the annihilations. Given that the fragmentation process between quarks and antiquarks is fairly understood, the spectra of gamma rays that are produced from their interactions can be predicted. Alternatively, gamma rays could be directly emitted by the WIMPs, with the rays being directly proportional to the mass of the WIMP. Though the order of magnitude of the flux from these gamma rays is difficult to detect, scientists remain motivated to utilise these methods as successful detection would be a significant indication of WIMPs and their mass. [31] To be detected, the gamma rays would enter an indirect detection device where they are exposed to conversion foils that convert the rays into electron and positron pairs. By tracking the energies of these electron and positron pairs with calorimeters, the detection systems can deduce the energies of the gamma rays that caused them and therefore predict the WIMP mass. [32]
Other than being potential candidates for dark matter from the SM, neutrinos can also be utilised to detect WIMPs when they are released as annihilation emissions. The explanation for this is as follows: WIMPs lose minute amounts of energy due to the scattering of nuclei as they travel through the universe, causing them to slow down and gather at the centres of large bodies with great gravitational presences. These convergences result in regions of high WIMP density, where the WIMPs collide and annihilate frequently. The WIMP density continues to increase within these regions until the annihilation rate is in equilibrium with the capture rate. [33] Given this equilibrium, a constant flux (flow) of neutrinos is emitted and can be detected as they pass through the atmosphere. Specifically, these neutrinos will interact with hydrogen and oxygen molecules and produce highly-energetic electrons, muons, and taus. Within the medium of the atmosphere, these energetic products will actually travel at speeds faster than that of light (since light would be constantly absorbed and reemitted in this medium while these energetic products pass through with less obstruction) and emit Cherenkov radiation. Cherenkov radiation is a blue glow, seen in Fig. 5, resulting from particles travelling at faster than lightspeed, analogous to a sonic boom, and are visual indications of these neutrino interactions. [34] Fortunately, the sun itself is in this WIMP-annihilation-capture equilibrium, thus providing us with an accessible source of neutrino flux from WIMP interactions.
Fig. 5: An image of the Advanced Test Reactor at the Idaho National Laboratory that depicts the blue glow of Cherenkov radiation when particles travel faster than the speed of light in a medium. (Source: Fig. 1 in Citation [35])
A third byproduct of a WIMP annihilation that can be detected is antimatter. With the cosmological rarity of antimatter and our developed understanding of many astrophysical phenomena that produce antimatter, detecting it in an appropriate environment would be a strong indicator of dark matter particles. Although WIMP annihilations often do produce antiparticles, including positrons, antiparticles to electrons, and antiprotons, these particles are challenging to directly detect because they are charged. [36] As a result, unlike neutrinos and gamma rays, these charged antiparticles are affected by magnetic fields in space, resulting in scattering, and can also lose energy through inverse Compton and synchrotron processes. Inverse Compton scattering is the energisation of low-energy photons to the x-ray or gamma ray spectra; by energising these photons, the antiparticles lose energy. [37] Synchrotron radiation, the radiation emitted by relativistic particles travelling in spirals, also causes the antiparticles to lose energy as they move through space. [38] Due to the loss of energy and the spiralling propagations of the antiparticles, scientists find great difficulty in pinpointing the exact site of the WIMP annihilation and instead, study the flux of these antiparticles from the galactic halo as a whole.
3. Simulations
Astrophysical simulations play a key role in determining the validity of certain theoretical models through the analysis of their applicability in replicating observed results. Parallely, simulations are also used to predict or analyse certain cosmological situations with the aid of our established models of the universe so as to deepen our understanding of the characteristics of the cosmos. [39] In relation to the study of dark matter, given the lack of established knowledge about the concept, simulations are often used with the former goal: to assess the applicability of proposed theories. Simulations require certain initial conditions, including cosmological parameters derived from CMB findings among others, as well as particle properties for certain dark matter theories that are being tested (e.g. WIMPs, axions, sterile neutrinos, etc.). Along with this, simulations require certain frameworks to build off of, such as the N-body simulation which tracks the gravitational interactions between a large number of particles. [40]
Outside of directly testing how well certain dark matter theories would hold up under simulated conditions, simulations of our universe also have had significant impacts in determining some of the core characteristics of the cosmos. Specifically, modern simulations have revealed key information about the way structures in our universe formed, hence allowing us to devalue and substantiate certain dark matter theories depending on the structure formation they permit. [41]
V. Implications of the Evidence, Past and Potential
1. Past Implications
A. Past Observation Results
Astrophysical observational results have had significant impacts on our understanding of dark matter as a whole but have particularly devalued the applicability of MACHO theories, essentially entirely validating the WIMP-approach to dark matter. Despite this however, observational results have also had potentially negative impacts on neutrino-based theories as well as the axion as a dark matter particle.
Firstly, evidence from the aforementioned Bullet cluster and its collision with the 1E 0657-56 cluster significantly devalued the MACHO dark matter theories. Studies of this collision showed that the collision resulted in the hot gas, the baryonic mass, within the galaxies of the cluster to be compressed and shock heated, releasing large amounts of X-ray radiation. The location of the source of this radiation was found in order to deduce the location of the majority of the galaxy’s baryonic mass. In parallel, gravitational lensing, the warping of space-time due to high mass objects, was used to deduce where the majority of the galaxy’s total mass was. When the results of these two deductions were cross referenced, a clear discrepancy was seen: the majority of the mass in these structures was non-baryonic. [42]
Furthermore, observational results from the COBE and WMAP satellites have revealed pertinent information regarding the characteristics of dark matter. One of the key CMB values measured by the COBE was the ratio of deuterium particles to hydrogen particles (D/H ratio) in the early stages of the universe. Modern evidence then showed that this D/H ratio is actually directly related to the density of baryons in the universe in the following equation:
where ΩB is the baryon density and h is a reduced version of Planck’s constant. The figure found for ΩB ended up only accounting for around 20% of the total density of the universe, indicating the vast majority of matter in the universe was non-baryonic. [43]
With certain anisotropies (fluctuations) being detected by the COBE within the CMB data, the WMAP was launched in 2001 to specifically study these anisotropies. The results from the WMAP corresponded with the results from the COBE and detected the discrepancy in baryonic density and total density to a greater degree of accuracy. The final density results detected by the WMAP can be represented as D/H ratios:
where ΩM is the total density and ΩB is the baryonic density. This discrepancy, seen in Fig. 6, shows that 83% of matter, the dark matter, in the universe is non-baryonic, thereby further devaluing the MACHO theories. [44]
Although these results have substantially relegated MACHO theories and at first, seem to point towards WIMPs as dark matter, the WMAP results also inflicted negative impacts on certain WIMP theories for dark matter. In particular, the D/H ratio calculated above by the WMAP findings is larger than neutrinos can account for. Given that the neutrino mass is constrained to < 0.23 eV, if neutrinos truly were the only dark matter particle in the universe, then the density of the universe would be ΩMh^2 < 0.0072, disagreeing with the WMAP findings seen in Fig. 6 and meaning that neutrinos cannot account for all dark matter in the universe. [44]
Fig. 6: A graph comparing the density of total matter in the universe to the density of baryonic matter, as detected by the WMAP. These are also compared to the projected total density if neutrinos were to account for all dark matter. (Source for data: Citation [44])
© Kabeer Hans, 2024
In relation to axions, Buschmann and collaborators attempted to connect astrophysical observations to the results that would be seen with the Peccei-Quinn symmetry that results in axion particles. Buschmann et al. focused on the cores of neutron stars to potentially detect axion bremsstrahlung. Bremsstrahlung, also known as “braking radiation”, is the emitted radiation from electrons that are deflected in fields of charged particles. [45] In the case of axions, this would serve as an indication of the conversion of axions into photons within the x-ray spectra. However, the x-ray readings detected from multiple neutron stars have been excessively high, to the degree where the readings cannot be solely explained by axions, thereby failing to validate the theory. [46]
In fact, recent observational results have even arrived at conclusions that dark matter may not be represented by axions, or more generally, by light supersymmetry particles. The study, carried out by Ng et al. in 2021, proposed that if dark matter bosons like the axion were to exist, then their presence could be detected by analysing their influence on rotating black holes. Ng’s study suggested that by capturing these particles, rotating black holes would slow down, but after analysing the black hole merger results from the Laser Interferometer Gravitational-wave Observatory (LIGO), they found that the high rotation speeds of these black holes were inconsistent with the potential existence of axions. [47]
B. Past Detection Results
i. Direct Detection
While they have aided in constraining some of the characteristics of certain dark matter theories, it is perhaps unsurprising given their ambitious goal to directly detect dark matter that no direct detection techniques have yet been successful in validating any of the leading conjectures. Recall that the two main direct detection methods within the field of dark matter include the attempts to directly detect WIMPs with sensitive systems and to detect the photonic conversion of axions in ADMXs. As previously stated, the leading direct detection experiments are the CDMS, the XENON10, and the ZEPLIN-I. All three of these systems were unable to detect WIMPs but all three managed to place upper limits on certain features of dark matter, as unsuccessful attempts to detect WIMPs in certain conditions can potentially rule out these conditions as dark matter particle environments. [27, 28, 29] Similarly, the ADMXs have not been able to produce conclusive indications of axions through photonic conversions but also placed restrictions on the properties of axions, such as their mass and coupling strength. [30]
ii. Indirect Detection
Although the indirect detection results have not managed to definitively validate any dark matter theories, they have been undeniably more successful than direct detection methods in substantiating certain conjectures. Recall that the indirect detection methods for detecting WIMP dark matter focus on the byproducts of WIMP annihilations, particularly gamma rays, neutrinos, and antimatter evidence.
In reference to the search for excess gamma rays that are possibly indicative of WIMP dark matter annihilations, the indirect detection methods have not provided any substantiating evidence. One of the most promising detectors is the Fermi Gamma-ray Space Telescope which, after surveying regions including the Galactic Centre and dwarf spheroidal galaxies, is yet to find excess gamma rays indicative of WIMP annihilation. [48]
Detection sites aimed at detecting neutrinos however, have seen greater success in recent times despite the early negative results. These early results were those from the AMANDA-II detector, located 1500 to 2000 metres underneath the Southern Pole, and the Super-Kamiokande (Super-K) detector, located in the Kamioka-Mozumi mine in Japan. The former of these two was focused on detecting a substantial neutrino flux from the sun that would indicate the sun to be in the WIMP annihilation-capture equilibrium previously discussed. Unfortunately, the AMANDA-II detector found discrepancies in its findings (which will be further discussed in Section V. 2. B. ii.) and was unable to obtain conclusive results that would aid neutrino-dark matter conjectures. However, the AMANDA-II was able to constrain certain characteristics of possible neutrino dark matter that would refine future searches. [49] The latter of these two, the Super-K detector, focused on not only the sun as a source of neutrino flux from WIMP annihilation but also concentrated on the galactic centre as a possible source. Like AMANDA-II, the Super-K detector has not obtained conclusive evidence favouring the existence of neutrino dark matter. [50]
Despites these initial failed attempts, the IceCube detector in Antarctica was successful in detecting cosmic neutrinos, the first-ever detection of high-energy neutrinos from deep-space sources that could be sites of WIMP annihilation. These detections were a significant development in neutrino astronomy and definitely strengthened the WIMP theories for dark matter. [51]
More success from indirect detection techniques was obtained by the HEAT Collaboration in the search for antimatter byproducts to validate WIMP dark matter conjectures. Specifically, the HEAT results detected an excess of cosmic ray positrons at energies of around 10 GeV, agreeing with hypothesised results from neutralino annihilations. [36]
C. Past Simulation Results
Findings from simulations based on established models of physics have had mixed implications on dark matter conjectures, particularly for neutrino and Kaluza-Klein theories. Regarding neutrinos as dark matter, simulation results reported by Paduroiu et al. have documented the structure formation in the early universe given our understanding of matter distribution and physical models. The simulations showed that structure formation was likely “bottom-up” formation, where smaller structures, such as stars and stellar systems, are formed before larger structures, such as galaxies and clusters. However, when these simulations were run with neutrinos accounting for all dark matter in the universe, this “bottom-up” structure formation was restricted by the fact that neutrinos are relativistic: they travel at speeds around the speed of light. This would classify neutrinos as “hot” dark matter and result in a “top-bottom” structure formation that our current models disagree with. [41]
Simulations that ended up favouring the Kaluza-Klein conjectures for dark matter were documented by Servant and Tait in 2003. The results of the study asserted that a LKP with a mass between 500 and 1200 GeV could be a possible dark matter candidate. They utilised theoretical calculations along with simulations that implemented the Universal Extra Dimensions (UED) framework to run predictions on the behaviours of particles in a proposed “LKP-dark matter” universe. The results have aided Kaluza-Klein dark matter conjectures, possibly validating the rather confrontational multi-dimensional approach. [52]
2. Potential Implications
Having established how empirical evidence has priorly affected dark matter theories, we will now analyse potential future implications of results to highlight the necessity for extended research and experimentation in the field of dark matter to formally assess leading conjectures.
A. Potential Observational Results
Though the field of observational astrophysics grows increasingly saturated, extensions to our current models of physics and solutions to dark matter could still be found through observation results. A potential source of further observational evidence in the dark matter field is the James Webb Space Telescope (JWST) launched in 2021 with the core goal to “shed light on our cosmic origins”. The primary capability of the JWST is to conduct infrared observations for detailed imaging and spectroscopy, which has already enabled some key contributions. [53]
In terms of aiding the search for a definitive dark matter theory, the JWST has immense potential. To elaborate, the JWST can provide insights into the early universe, studying formation of primitive galaxies and stars to infer dark matter distribution, and analyse strong and weak gravitational lensing effects to provide detailed maps of dark matter. Further, the JWST can observe dark matter halos around galaxies, aiding in investigations of galactic dynamics that are influenced by dark matter, and provide complimentary data that can be cross-referenced with other dark matter detection models as a way of assessing their validity. [54]
Therefore, results from the JWST can have significant implications towards dark matter conjectures, particularly WIMP theories that require increased evidence from deep-space interactions and annihilations to garner credibility.
B. Potential Detection Results
i. Direct Detection
Planned and partially executed improvements and refinements to direct detection facilities across the globe have made the prospect of further assessing dark matter theories through this ambitious approach more likely. With facilities aimed towards detecting axion activity and WIMP activity both set to receive upgrades and be set into operation in the near future, implicative results may imminently arrive for both these theories.
The ADMXs previously discussed, which were unable to detect the photonic conversion of axions, are set to be upgraded to ADMX-IFs (improved filters), with the receptors and amplifiers depicted in Fig. 4 having increased sensitivity and responsiveness. [55] Along with this, the CERN Axion Solar Telescope (CAST) could also significantly contribute to the axion dark matter theories as it focuses on the sun as a potential site of axion activity through the aid of LHC dipole magnets and cryogenic technology from the DELPHI experiment. The CAST utilises a strong magnetic field from a superconducting magnet to convert axions into detectable X-rays, having potentially immense implications on axion theories for dark matter. [56]
Akin to the ADMXs, direct detection facilities for WIMP dark matter are also set to receive upgrades and improvements. The XENONnT is a proposed upgrade to the XENON1T, which was unsuccessful in detecting WIMPs, that is set to improve the sensitivity to WIMP dark matter by a large magnitude through a larger active mass, a significantly reduced background, and improved veto systems. [57] Furthermore, the ZEPLIN-I experiment is set to be upgraded to the LUX-ZEPLIN (LZ), a xenon-based WIMP detector on a much larger scale than its predecessors. The LZ is set to begin data collection in the near future and through its substantial improvements, including auxiliary veto detectors to improve the rejection of unwanted background in the central region of the sensor, is projected to improve upon the sensitivity of old generations by at least a factor of 50. [58]
ii. Indirect Detection
Indirect detection continues to be the method of obtaining empirical evidence with the greatest potential of substantiating WIMP dark matter theories. Extensions to the search for WIMP annihilation byproducts (gamma rays, neutrinos, and antimatter) can heavily affect leading theories, particularly SUSY neutralinos, as candidates for dark matter.
A detection site with great potential in the search for dark matter signals is the Cherenkov Telescope Array Observatory (CTAO), named after the aforementioned Cherenkov radiation that can potentially serve as a sign of dark matter activity. The CTAO is primarily focused on detecting gamma rays, through the process seen in Fig. 7, with the site being the largest and most sensitive ground-based gamma ray observatory. The CTAO detects gamma rays from the highest energy sources in our known universe and aims to improve the search for dark matter annihilation byproducts from the galactic centre and dwarf galaxies. If found, conclusive results from the CTAO would be vital in validating WIMP theories for dark matter, our current leading approach. [34]
Fig. 7: A graphic depicting the “Air Shower” of Cherenkov radiation that the CTAO aims to detect as a means of confirming cosmic gamma rays from WIMP annihilations. (Source: Fig. 2 in Citation [34])
Outside of improvements to existing detection sites or the establishment of modern facilities, extended studies of results from past indirect detection findings could themselves have significant impacts. In particular, physicists have identified a possible explanation to the deficits seen in the AMANDA-II results when searching for a neutrino flux from the sun (mentioned above). The recent studies assert that the AMANDA-II discrepancies were due to oscillations of muon neutrinos into “sterile neutrinos”. Sterile neutrinos are hypothesised to be “flavours” of neutrinos that do not interact through the weak force and only interact through gravity. Though sterile neutrinos are not currently found in the SM, their existence can explain the discrepancies in AMANDA-II data and make them a candidate for dark matter. Along with this, sterile neutrinos could also explain the matter-antimatter (baryon) asymmetry that we observe (the CP problem). This is by allowing leptogenesis, where lepton asymmetry leads to the observed baryon asymmetry, due to the decay of sterile neutrinos into neutrino flavours seen in the SM. This has strongly motivated the study of sterile neutrinos, with results from the Antarctic Impulsive Treatment Antenna (ANITA) presently being analysed to further assess sterile neutrinos as potential dark matter particles. [2, 59]
The pursuit in detecting antimatter as a byproduct of WIMP annihilation is also set to improve as the General AntiParticle Spectrometer (GAPS) is scheduled to begin operation imminently. GAPS is an Antarctic balloon that aims to detect low-energy cosmic antiparticles, specifically antideuterons, antiprotons, and antihelium particles, which have not been unequivocally detected before. The technique that the GAPS will look to utilise is to slow antiparticles in the tracker material and capture them with a nucleus that converts the antiparticles into exotic atoms. These exotic atoms then decay, releasing x-rays that are detected by the sensor and confirming the presence of antiparticles. This novel approach could prove to be strongly supportive for WIMP theories in the near future, following its successful prototyping (pGAPS) and launch scheduling for 2024. [60]
C. Potential Simulation Results
Simulations remain to be key methods of assessing the validity of our established models of physics as well as determining the applicability of new conjectures. Through simulations that map out and identify the composition of the universe given certain frameworks, various dark matter theories can be compared to the findings that are obtained.
A modern project that may have immensely consequential implications on dark matter simulations is the Euclid Space Telescope from the European Space Agency (ESA), a mission centrally focused on studying dark matter and dark energy. The Euclid Space Telescope uses weak gravitational lensing and galaxy clustering to map dark matter distribution in the universe. This could enable the creation of a precise framework that can be implemented into future simulations to test how well WIMP and Kaluza-Klein models agree with the observed results. [61]
Another project with the potential to aid future simulations of dark matter models is the Vera C. Rubin observatory. The Vera Rubin observatory is a ground-based observatory that will conduct a decade-long survey of the sky to study the distribution and, critically, the behaviour of dark matter in our universe. The observatory could make significant contributions to our understanding by creating high-resolution maps of dark matter through weak lensing and galaxy clustering, as well as test dark matter models, including WIMPs and axions, by analysing cosmic structures. Apart from running its own simulations, the Vera Rubin observatory, like the Euclid Space Telescope, can utilise its findings to create an accurate framework for future simulations to further assess dark matter conjectures. [62]
VI. Conclusion
Dark matter remains to be one of the most pressing unknowns in modern science, with its understanding and explanation being of utmost importance if our physical models of the universe are to progress further. Thereby, the multitude of radical theories attempting to explain dark matter are welcomed, as a solution to such a mysterious phenomena may very possibly come from an equally mysterious theory. In this review, we have analysed how dark matter conjectures have been both devalued and substantiated by empirical results, while also glimpsing into the proposed impacts that increased evidence may inflict. The field of dark matter only grows in pertinence and modern science will indefinitely continue to propose theories, confrontational if required, to solve one of the most enigmatic problems in physics.
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