Abstract – The existence of Dark Matter is widely accepted in the scientific community, but its identity is still an enigma. Numerous independent gravitational observations seen cannot be explained by the Newtonian mechanics of the visible mass. A rather simple hypothesis suggests the existence of new particle or particles, termed as Dark Matter, to give a rationale for these observations. This paper seeks to give a comprehensive overview on the existing theories of dark matter candidates and the status of the dark matter search. This review begins with a description of the Standard Model of Elementary Particles followed by a brief discussion on the principle problems unexplained by this model. We then compare the theoretical predictions with the actual galactic rotation curve of the Andromeda Galaxy and its scientific implications, supporting the claim that dark matter exists. We investigate the prominent dark matter models including WIMPs, Axions, and Sterile Neutrinos, critically examining each of their theoretical motivations, production mechanisms, characteristics, and interactions with the standard model. We also explore a wide range of their direct and indirect detection methods- particle colliders, astronomical observations and data, advanced detectors, and many more- in detail. Furthermore, we give the reader insights into selective experiments being conducted that claim to give possible signals of dark matter. We conclude our paper with a discussion of contemporary and upcoming experiments to detect dark matter. Future experimentation will be critical to the development of this field. Old and new candidates will inevitably be ruled-out and developed as dark matter theory and detection methods continue to progress forward.
Index Terms – Dark matter(353), Dark matter detectors(355), Galaxy rotation curves(619), Particle astrophysics(96).
One of the longest-standing questions in physics is about the composition of our universe. Right after the Big Bang, the universe was very hot but subsequently began to expand and cool down. Due to this, particles collided less and acquired a fixed number density, which is a measure of the concentration of particles. Visible or baryonic matter, which constitute all the galaxies and stars, accounts for only 4.9% of the total matter in the universe. The rest of the universe is made up of Dark Matter (26.6%), matter we cannot see as it does not scatter light, and Dark Energy (68.5%), which is mysterious energy that accelerates the expansion of the universe.
Dark matter is colloquially known as “missing mass” because without it, several issues arise throughout the field of astrophysics. Calculations for Galaxy Rotation Curves show that the rate at which many galaxies rotate is not consistent with their observed mass: they would be torn apart, should not have been formed, or should not be moving at the speed they do. The calculated center of mass of the Bullet Clusters, which is an imaginary point where the total mass of the result of the collision of 2 galaxy clusters can be assumed to be concentrated in, is far away from its baryonic centre or its visible matter centre. The difference in the predicted and observed center of mass is suggestive of additional material. This, like physical theories surrounding gravitational lensing, the Cosmic Microwave background, the structure of the universe, and the formation and evolution of galaxies, is where dark matter comes in.
Dark matter was first discovered by the Swiss Astronomer Fritz Zwicky. It is “dark” because it does not appear to interact with the electromagnetic radiation, and is Matter because it interacts with baryonic particles via the gravitational force and therefore contains mass. Dark matter is very stable, as it has existed since the Big Bang, which occurred 13.772 ± 0.040 billion years ago. Current evidence suggests that dark matter particles either do not interact with one another or do so weakly. Various models debate on whether dark matter is cold, hot, or fuzzy. These monikers do not refer to the particle’s temperature; rather they are properties that describe its speed as compared to the speed of light. According to the prevailing λ-CDM (Lambda cold dark matter) model, dark matter is most likely cold, slow moving, and nearly collisionless. If dark matter is hot, then its speed would be comparable to cx m/s. Fuzzy dark matter is an intermediate candidate between the two. Galaxy formation in the early universe under these scenarios is illustrated in Figure 1.
If early galaxies were formed under the CDM model, they would first form spherical halos or clumps that merge and give shape and structure to it, as shown in the first simulation. In a hot dark matter universe, galaxies are likely to be formed with filaments because particles, being lighter, would be moving fast and not form clumps, as represented in the middle figure. Lastly, if there was fuzzy dark matter, striated tail-like structures would form, which is depicted in the last figure (Chu 2019).
Candidates for dark matter include non-baryonic hypothetical particles such as weakly interacting massive particles (WIMPs), axions, sterile neutrinos, neutralinos, cold dark matter, hot dark matter, supersymmetric particles, gravitationally-interacting massive particles (GIMPs), gravitinos, geons, and baryonic structure like MACHOS and primordial black holes, as seen in figure 5. The candidates are characterised on the basis of their mass and coupling strength, a parameter related to their probability of interacting with the standard model. Although each of these models have many interesting aspects like the light gravitino warm dark matter being a natural consequence of supersymmetry breaking models, we will only focus on the few most prominent models.
Detection of dark matter can be direct or indirect. Direct detection methods refers to directly looking for dark matter particles or its decay products (which are particles obtained on the decomposition of dark matter), while indirect detection refers to using scattering experiments to find traces suggesting the presence of some unknown dark matter. For instance, in direct detection, heavy metals like lead are isolated for a long time period where underground detectors aim to detect some extra energy when dark matter interacts with the metal. This, however, has very low probability. On the contrary, in indirect detection, collisions of particles like photons take place in the particle colliders and physicists account the missing energy and momentum as effects caused by dark matter. In other words, in indirect detection, physicists observe other particles getting momentum because of the dark matter particle scattering.
This paper attempts to answer the stated question: What theories can help us understand the candidates for dark matter, and what experimental techniques could be used to detect dark matter? This paper seeks to examine 3 major models proposed for dark matter, namely WIMPs, Axions, and Sterile Neutrinos, in order to understand current theoretical frameworks for dark matter. In Section 2 we briefly review the Standard Model, a necessary prerequisite to understanding the theoretical backings of dark matter, and a few problems it does not address. In section 3 we conduct a brief simulation of galactic rotation curves, providing a simple validation of the necessary presence of dark matter in our local universe. In section 4 we scrutinise the most prominent dark matter candidates, examining their physical properties and discussing how they account for discussed gaps in the Standard Model. In section 5 we explore their direct and indirect methods of detection. And finally, in Section 6 we conclude by summarising the results and the discussion and expounding on the implications of the discussion presented in the paper along with some future steps.
II. THE STANDARD MODEL
Standard Model of Elementary Particles: the quarks are marked by the purple colour, leptons by green, spin 0 gauge bosons by red, and spin 0 gauge bosons by yellow colour (Cush 2018).
The Standard Model of Particle Physics is an extremely successful, well-tested physical theory that explains the interactions of the fundamental/elementary particles, or basic building blocks of matter, and the 4 fundamental forces governing them. All fundamental particles are separate; none of them compose the other. Particles are divided into fermions(the matter content) and bosons (the force carriers).
Fermions are particles that make up matter and have fractional spin or rotation, which is a measure of its angular momentum. Baryons, the subatomic particles that constitute almost all the matter we encounter daily, are also classified as strongly interacting fermions. Fermions are further classified as quarks (up, down, charm, strange, top, & bottom) and leptons (electron, muon, tau, electron neutrino, muon neutrino, & tau neutrino). According to Pauli’s Exclusion Principle, which states that each femion has a unique set of quantum numbers in an atom, fermions do not share their state: only a single fermion can exist in a principal quantum state. For a more detailed discussion of the nuances of fermions and leptons, see Ref. .
Bosons are the “force mediators” and have integer spin. The spin 1 gauge bosons include photons, 8 gluons, and the W & Z bosons. Photons mediate the electromagnetic force. Gluons carry the strong force which holds the nucleus together. The W & Z Bosons carry the weak force which helps in the decay of the nucleus. The Gravitational force is the weakest of all the fundamental forces but acts up to an infinite range. Its effects increase as the mass of the object increases. It is not explained in the standard model: at the macroscopic scale, Einstein’s General Theory of Relativity explains that gravity is caused by the distortion or bending of space-time due to an object with mass. The recently discovered Higgs Boson has Spin 0. The Higgs particle is a wave of minimum energy that depends on space and time. Just after the Big Bang, all particles were massless and moved at the speed of light. During this primordial stage, the Higgs Field started changing the particle’s behaviour giving them mass. All known fundamental particles interact with the Higgs Field to get their mass. The Higgs field, unlike other fields, does not hold zero energy on average; otherwise no atoms, and thus no ordinary matter would exist. More precisely, the non-zero value of the Higgs Field’s equilibrium constant has given mass to the particles of other fields. In conclusion, particles interacting more strongly with the Higgs, such as the down quarks, have more mass. For more information on the Higgs Boson, check Ref. . Additionally, bosons don’t share their state, for example, in the light particle photons. All elementary particles of the standard model are mentioned in Figure 2.
Nonetheless, the standard model is incomplete. 3 leading problems in particle physics which encompass primary gaps in the model are encapsulated below:
The Gauge Hierarchy Problem
The mass of the Higgs boson was predicted to be approximately 1.2 x GeV, but it was actually found to be of the order GeV. The Gauge Hierarchy Problem refers to why there is such a large difference in the expected and experimental values of the Higgs mass. More precisely, through quantum mechanics, the size of the Higgs field should either be zero or be extremely large- of the order of the Plancks Energy. But, it is found to be very small and close but not equal to zero. This discrepancy is related to the non-zero Higgs field, which consequently determines the mass of the W & Z gauge bosons. Dark matter candidates like WIMPS, superWIMPS, light gravitinos, and hidden dark matter tackle this problem. We elaborate how WIMPs propose to solve this problem in section IV (A).
The Strong CP problem
The Strong Charge-Parity (CP) problem is the question of why the CP is conserved by strong force. Charge conjugation refers to the operation of replacing particles with their antiparticles that have the opposite charge. Parity transformation refers to the process of flipping the sign of a spatial coordinate for a particle or inverting the chirality of a particle. Chirality is a property that signifies the superimposability of a particle on its mirror image or, more technically, the rotation of the plane polarised light by a particle. If charge conjugation and parity transformation could be applied to a particle, then its collision would still look the same. Physically, it means that the collisions of quarks and antiquarks would look the same if time were to run backwards. In other words, the strong nuclear force would affect both quarks and antiquarks in the same way if they were on the opposite sides of a mirror. As a result, input parameters of the Standard Model were severely restricted and needed to be fine-tuned to fit a theory or observation. Axions are hypothetical particles proposed by the Peccei-Quinn Theory that can solve this problem. We discuss this further in section IV (B).
The Neutrino Mass Problem
Neutrinos are negligibly interacting, uncharged particles that have extremely small mass which does not come from the Higgs boson. In order for a particle to have mass by the higgs mechanism, it should have both right and left-handed neutrino fields. Handedness relates the direction of a particle’s spin to the direction which it’s travelling in. Curling one’s fists with their thumbs pointing outwards is considered a good representation of this concept. Neutrinos only have left handed configurations. If they had both LH and RH, then they would not travel at the speed of light. This is necessary as boosting beyond the speed of a neutrino is needed to effectively flip the observed handedness of the neutrino. A possible source of neutrino mass is from the seesaw mechanism in which the product of the left handed and right handed masses comes out to be a constant. They are formed during 𝛽 – decay (n→ p + e +𝑣).This is the neutrino mass problem. Sterile Neutrinos are proposed dark matter candidates that resolve the neutrino mass problem. This is discussed in section IV (C).
Dark matter candidates have the potential to fill these gaps in the standard model. For instance, light gravitinos and hidden dark matter address the New Physics Flavour Problem. Thus, having evidence of dark matter is essential towards solving for the incompleteness of the standard model, relative to the as of yet undiscovered Theory of Everything (ToE).
III. GALAXY ROTATION CURVE: ANDROMEDA (M-31) GALAXY
A Galaxy Rotation Curve is a plot of the orbital velocities of visible stars and gas in a galaxy versus their radial distance from the galaxy’s centre. It’s one of the most compelling pieces of evidence for dark matter. Astronomers Vera Rubin and Kent Ford measured the galaxy rotation curve and found that visible matter does not account for the velocity of the stars at the edge of the galaxy, which is greater than the predicted velocity. The visible baryonic matter decreases when moving radially outwards from a galaxy’s centre. And according to Newtonian Mechanics, this matter provides the gravitational pull and the centripetal acceleration of the stars and gases. This implies that the orbital velocity of the stars should also decrease. However, observations indicate that the velocity grows approximately linearly with the radius and even beyond the location of most stars (galactic bulge). Thus, there should be more non-visible mass to account for the high velocities in the galaxy rotation curve problem. When this “extra” mass of the “dark matter halo” is added to the calculations, these higher than expected galactic rotation velocities can be explained.
DATASET: ANDROMEDA M-31 GALACTIC ROTATION
The experimental data to plot the curve for the standard mass + dark matter are taken from Ref. .
The fixed values of the constants to calculate the standard mass plot are from Ref. .
GALACTIC ROTATION CURVE SIMULATION
In this paper, we create a simulation to model rotational velocities for the standard model mass distribution and dark matter plus the standard model mass distribution in the Andromeda galaxy. The simulation is conducted using python in Jupyter Notebook. We make use of python libraries matplotlib, numpy. The dark matter halo is taken to be a perfect sphere. The standard mass of this spiral galaxy is considered to be a perfect disk of finite radius R. Uniform mass density throughout the galaxy is assumed. The plot visualises the relationship between the radius r of the galaxy in kiloparsecs and the velocity v(r) of the stars in kilometres per second.
If there is no dark matter, then the mass of the galaxy contained in that radius r should increase as the volume increases and then become constant after reaching the edge of the galaxy. So, in order to calculate the mass, we integrate over 0<r<R and take the total fixed mass M of M-31 for r=R and r>R. We note that the M-31 galaxy has radius (R) 33.5 kpc and mass (M) 5.0 x kg.
Let m be the mass of the testing object orbiting around the galaxy with velocity v(r) on which the centripetal force that is caused by the gravitational force acts.
But, = m (3)
In the above equations, G is the universal gravitational constant, m is the mass in the galactic halo and, as discussed, r is the distance from the galactic centre.
The blue dotted curve in Figure 3 is obtained following the above calculations using the known baryonic mass observed up to radius r.
However, observed values for the rotation curve velocity, plotted as a function of radius in green in Figure 3, do not conform to these expectations.
Without dark matter or additional mass, then the v-r relationship should follow the blue-curve, increasing steadily until r>R, at which point the radial velocity should begin decreasing. We observe in Figure 3 agreement in the predicted and observed radial velocities only around r=R; for all other distances, observed velocities significantly exceed the predicted values. This indicates a gap in the model, which can most readily be explained by some “missing mass”. Thus, our simulation clearly supports the claim that dark matter exists.
M-31 GALACTIC ROTATION CURVE
The different colours indicate the different types of dark matter models classified on the basis of their characteristics. Dark matter is often integrated with various theories like those of extra-dimensions, supersymmetry (susy), quantum chromodynamics, and modified gravity (CERN, n.d.).
Numerous dark matter candidates have been suggested, as can be observed in Figure 4. In this paper, we focus on 3 leading candidates which are actively being theorised and are the focus of detection experimentation. We discuss these three candidates in the following order: WIMPS, Axions, Sterile neutrinos.
WIMPs are a class of hypothetical exotic particles that includes several proposed particles such as massive Dirac neutrinos, cosmions, and SUSY relics. WIMPs are “weakly interacting” and have no effects on baryonic matter. Their predicted mass is approximately 100 GeV, which is similar to the mass of the Higgs boson. Consequently, these particles travel very slowly, making them a type of cold dark matter. WIMPs have tree level interactions with the W & Z gauge bosons. Tree level interactions are those interactions that are more probable or likely to occur. This is represented in Feynman diagrams that have no loops. An example Feynman diagram is in figure 5. Despite their elusive nature, WIMPs are one of the most hunted particles because they have the correct relic density, a fact sometimes referred to as the WIMP Miracle. Initially when the universe was hot and dense, all particles were in thermal equilibrium. But, the universe was simultaneously cooling and expanding, resulting in the dark matter particles to become so dilute that they couldn’t find each other to annihilate. Thus, the number of dark matter particles became constant with this number – their relic density – accurately accounting for the dark matter content now.
Moreover, WIMP-like particles also come up in particle physics theories like Supersymmetry (SUSY) that offer to resolve the gauge hierarchy problem. For more information on Supersymmetry, refer to Ref. . They are being searched for using direct dark matter detectors and particle colliders like the Large Hadron Collider. The DARWIN experiment is one of the most advanced experiments searching for interactions with dark matter in vats of supercooled Xenon. A large tank of supercooled Xe is taken to increase the probability of including dark matter in it. As Xe is denser, the gain in xenon’s momentum due to interactions with dark matter would be more easily observable and probable due to more particles in denser substances. A challenge to designing WIMP direct detection experiments is that it should simultaneously be sensitive to a few keV of energy depositions and contain a large mass of detectors. Furthermore, it should have excellent background rejection and eliminate any other background frequencies/noises like those of electron recoils. Since neutralinos are their own antiparticles, they can annihilate each other to produce high energy neutrinos that could be detected on Earth. WIMPs moving in the galactic halo would be gravitationally focused towards the Sun where they would be captured through collisions with atoms in the Sun’s centre. WIMPs in the galactic halo could also annihilate into electrons, protons, photons and each of their antiparticles.
Axions are theorised spin 0 particles which are electrically neutral. Their predicted mass is less than 1eV, which makes them look like waves (Wave-particle duality: every quantum entity may act as both a particle and a wave). This is necessary as the mass of an axion is directly proportional to the CP violation and therefore should be extremely small. Classification of axions as cold or dark hot matter depends on the determination of their mass, which is as of yet undetermined. Although axions are super light, they would have been produced abundantly in the Big Bang. They have very weak interactions with gamma rays (photons), gluons and fermions. Axions are thought to be created by photon conversion: a photon and a photon from a magnetic field combine their energy to produce an axion. Figure 5 represents this interaction.
This Feynman diagram represents the process of photon conversion. The double lines portray the electromagnetic field from which a photon (wavy line) emerges. It combines with a regular photon to produce an axion (dashed line). We could also look at this diagram in a way such that an axion and a photon form a magnetised photon that could be easily detected (CERN, n.d.).
In addition to solving problems in nuclear physics and the Strong CP problem, they also could help explain the abundance of matter as compared to antimatter. It is proposed that a few billionth seconds after the Big Bang, θ ,the angle in the equations describing the strong forces, may have cycled between 0° and 360° before settling down on the angular position of 0° for minimal energy to be consumed. Consequently, the axion field would have rotated. The frictional force by other matter fields would in turn result in the remaining kinetic energy to be utilised in generating new particles, leading to the matter-antimatter asymmetry.
Current searches for axions include laboratory experiments using sensitive equipment like sensors and antennas, and searches in the halo of our Galaxy and in the Sun. The CERN Axion Solar Telescope and IAXO are axion helioscopes that aim to detect axions produced at the solar interior. ALPS in DESY and OSQAR at CERN are using intense magnets to detect axions produced during photon conversion. Another interesting experiment is the ADMX that is using strong magnetic fields and microwave cavities to convert undetectable axions to microwave photons.
C. Sterile Neutrinos
Neutrinos have a mass very close to 0, but in the standard model they were thought to have no mass. This is called Neutrino Oscillations. Sterile neutrinos are a class of theoretical fundamental particles that were proposed to explain the oscillation effects that required more than the 3 active neutrinos- electron, muon, and tau neutrino. Because sterile neutrinos have a non-zero mass and no electromagnetic charge, they are considered as possible candidates for dark matter. They are sterile because, unlike the other neutrinos that interact with the weak and gravitational force, sterile neutrinos only interact with gravity. This and the fact that sterile neutrinos have a very small mass make them extremely difficult to detect. They are, thus, called “sterile”. To date, only left handed neutrinos and right handed antineutrinos have been found. But, since the weak force strongly prefers to interact with left-handed particles, sterile neutrinos are thought to be the right-handed neutrinos. They are light because otherwise there would be excess energy in the dark matter sector than observed as energy is equivalent to mass by the equation where momentum is denoted by p.
However, sterile neutrinos belong to the neutrino family and retain certain essential properties. Neutrinos oscillate and change their types/flavours while travelling. In other words, while oscillating, one kind of neutrino can change into another type. So, for example, an electron neutrino could turn into a sterile neutrino that would make it seem like it disappeared or account for the rapid changes and experimental anomalies. While studying the decay-at-rest beam made of mainly the muon neutrinos at the Liquid Scintillator Neutrino Detector (LSND), more than predicted number of electron neutrinos was found which could be attributed to the sterile neutrinos. Some experiments like the MiniBooNE experiment at FermiLab have seen excess neutrino oscillations than predicted in theories. On the other hand, the MINOS experiment, the IceCube experiment, and the Daya Bay Reactor Neutrino Experiment found no signals of sterile neutrinos. However, in order to arrive at a concrete conclusion, more research needs to be done. They solve the neutrino mass problem as they are assumed to have both RH & LH and may help to address the origin of matter-antimatter asymmetry.
Dark matter is one of the components of our mysterious universe that has been only detected through its gravitational interactions with baryonic matter. We need dark matter to explain strange phenomena including bullet clusters and galactic rotation curves. All dark matter is thought to be composed of baryonic as well as non-baryonic particles.
The Standard Model elucidates on the known particles and forces in nature. But, like any other theory, it also has gaps. We summarised the key features of the standard model and some of its most pressing limitations, including the Neutrino Mass Problem, Gauge Hierarchy Problem, and Strong CP Problem. Perhaps related to these problems directly, the Standard Model does not account for dark matter.
Dark matter is relevant because its evidence is evident everywhere, hence a need to address these gaps in the Standard Model. In this paper, we performed a simulation of the galactic rotation curves seen in the Andromeda Galaxy. The results demonstrated that the difference in the experimental and calculated curves can be understood by considering dark matter in our calculations, providing for our reader robust but simple evidence supporting the existence of dark matter within the Universe.
With this simple verification of dark matter’s presence, we then assessed eminent contemporary theories for dark matter candidates. We noted that weakly interacting massive particles, a type of cold dark matter, have the correct relic density, are predicted by the supersymmetry theory, and are a natural consequence when solving the hierarchy problem. Assumed to be in a mass range of 2GeV to 100TeV and interact weakly with W & Z gauge bosons, they are extensively searched for in particle colliders during 𝛽-decay. Axions, in contrast, are superlight spin 0 exotic particles that have weak interactions with photons, participate in photon conversion, and aim to solve the strong CP problem. Experiments like the ADMX are looking for them. Lastly, the motivations for sterile neutrinos are that they elegantly solve the neutrino mass problem being right handed, and we also may find them sooner than the other candidates. Carefully studying neutrino oscillations is an excellent method of finding their traces.
While much of dark matter research remains purely theoretical, physicists are actively trying to search for signals or signatures of dark matter particles in various mass ranges using the properties shown by the proposed models. The hints of dark matter are being identified by essentially “making it, breaking it, or shaking it” or colliding protons at the LHC, observing the particle annihilation, and running sophisticated tests underground to find some extra or missing physical quantities (like momentum) in the atomic nuclei of isolated heavy metals. Furthermore, many new theories, for example the theory of modified gravity, idea of hidden valleys of dark matter, string theory, supersymmetric extensions to the standard model, idea of extra dimensions, and the Theory of Everything, are also being postulated to yield answers to this puzzling quest. Future prospects could analyse how the different candidates of dark matter behave under the conditions of a particular model/theory of dark matter. Building stronger and more sensitive particle colliders than the LHC could also aid in dark matter searches. A complicated model with more species of dark matter that will have complex dynamics and self-interactions could also be proposed. We also need to collect and analyse more cosmological data. More research on dark matter has the potential to lead us to a whole new era of physics wherein we are successfully able to go beyond the standard model and revolutionise this field of study.
Thank you for the guidance of Cari Cesarotti & Tyler Moulton from Harvard University in the development of this research paper.
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Ishika Gupta is a senior at Modern School Vasant Vihar, New Delhi, India. She is passionate about solving the mysteries of the universe. Ishika enjoys listening to music, playing the piano, painting, and playing soccer. She is a family-oriented girl. She likes celebrating all festivals and never misses an opportunity to interact with people. Ishika loves learning new things and is eager to expand her knowledge of cosmology, astrophysics, and particle physics via research.