Quantum Fields, Gravity, and the evidence for non-baryonic particles
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One of the oldest projects in science involves constructing a fundamental ontology. The scientist aims to create a comprehensive model of the world, in which no phenomena is left unexplained. New models are deemed successful if they continue to increase the domain of our understanding. Physics is once again reaching a point in which our current theories require re-articulation. A certain class of astronomical observations continue to elude explanation, namely, that strong gravitational potentials exist in regions devoid of visible matter. This paper will be focused on introducing the primary evidence that supports these claims. However, I want to begin by briefly outlining the explanatory power of our current theories.
Particles and Fields
Quantum Field Theories are some of the most successful models of the universe to date. As the name suggests, the universe is described as a dynamical system of quantum fields. Each of these fields corresponds to a fundamental particle from the Standard Model. When a particle is localized, it is seen as an excited vibrational mode of its underlying field. The first quantum field theory pertained to the electromagnetic force, known as QED. From there, coherent field theories were developed for the other particles in the Standard Model. The chart below is one of the crowning achievements of physics, it lists seventeen classes of particles that account for almost every known interaction in the universe.
One of the key parameters used to distinguish these classes of particles is intrinsic angular momentum, called spin. Particles with half-integer spin are known as fermions, while integer spin valued particles are bosons. The strong, weak and electromagnetic force are all described as being interactions between fermions, mediated by the exchange of gauge bosons. Gravity has not yet been unified with this schematization, and is best described by the field equations of Einstein’s General Relativity. Gravitation is the dynamical curvature of space-time, altered by the energy-density of regions, and calculated using the metric tensor. An unintuitive consequence of this formulation is gravitational lensing. When making astronomical observations, photons from distant objects must travel large distances to reach us. If the regions they pass through are distorted by the presence of large amounts of mass-energy, then the photons trajectory becomes warped. This leads to highly distorted optical images, and can offer us important evidence as to how much matter this photon passed through on its journey to Earth. Lensing varies in strength, from dramatic images of the same celestial object appearing multiple times, to a slight, but consistent systematic alignment of objects that should be otherwise uncorrelated.
An important class of particles to our coming discussion are baryons. These include familiar particles such as protons and neutrons, and are characterized by a composition consisting of three quarks. When we typically refer to the substance of the universe, we mean baryonic matter. The entire periodic table, and the branch of chemistry, are devoted to the various configurations of this form of matter. However, it has been made increasingly plausible that the majority of the matter density of the universe is non-baryonic. This statement is corroborated greatly by the inexplicably strong gravitational potentials observed in space, and we may soon be forced to go beyond the Standard Model. I will now provide an overview of the evidence for this claim in order of scale: starting on the galactic level, moving to clusters, and then examining how this anomaly persists on the level of the universe at large.
Galactic Rotation Curves
The ability of astronomers to determine the chemical composition of distant stellar objects is largely due to a technique known as spectroscopy — which is a method of studying the interaction between matter and electromagnetic radiation. When gases are excited, the electrons transition between different orbital shells, emitting energy in the form of photons. The different energy levels of common gases, such as hydrogen and helium are well known and quantized. This means that the spectrum of visible photons emitted by a certain gas gives a distinct and recognizable pattern. With this knowledge, looking towards stars and planets, we should be able to determine their composition based on the pattern of visible light given off. However, it was observed that the entire emission spectrum of distant nebulae were redshifted. The best explanation for this occurrence was put forth by Edwin Hubble, who determined that the universe was expanding. This expansion rate is captured by the Hubble parameter. Spectroscopy, coupled with Hubble’s observation is one of the primary methods for determining the composition of celestial objects.
In many types of galaxies, orbiting bodies tend to lie in a thin disc, and move in circular trajectories around the galactic center. Measuring the orbital velocity of these bodies as a function of distance from the center gives us a galactic rotation curve. As you move away from the center of a galaxy, one would expect to see a Keplerian drop off. The orbital speed should initially rise, and then fall steadily as the radius gets larger. Given this relation, it seems straight forward to assume that you could derive the mass distribution of a galaxy from its rotation curve. Until the 1970’s, optical technology was limited, and only inner galactic discs of nearby galaxies had measured curves. For points outside the measured radius, Keplerian behavior was simply extrapolated. In Horace Babcock’s 1939 dissertation, he constructed a rotation curve for the M31 galaxy out to 20kpc. He noticed abnormally high orbital velocities at large radii, meaning high mass-to-light ratios were calculated for distant regions of M31. Vera Rubin and Kevin Ford published refined measurements of the M31 rotation curve in 1978, obtaining the first concrete proof that there was an unseen force causing the rotation curves to flatten out. Finally, Albert Bosma measured the rotation curves of twenty-five galaxies, all of which clearly showed no velocity drop off. To summarize the problem: given the number of visible celestial objects contributing to the gravitational potential of the galaxy, the outer stars were moving far too quickly. The gravitational field from the disc alone is too weak to provide the necessary acceleration for the outer stars. At this point, many independent experiments had corroborated the fact that the Keplerian prediction was no longer valid. Thus, the issue does not appear to lie with experimental precision.
Coma Cluster and Virgo Cluster
In 1933, when Fritz Zwicky released a paper entitled The Redshift of Extragalactic Nebulae. While making observations on the Coma Cluster, he noted a very large radial velocity dispersion among eight of its constituent galaxies. The dispersion was around 1000km/s — so high that it became curious as to how this apparently stable cluster remained gravitationally bound. While this dispersion had been previously noted by Edwin Hubble and Milton Humason in 1931, Zwicky went further and applied the Virial Theorem to obtain an approximation of the kinetic energy of the system. Using estimates for the number of observed galaxies, galactic masses, matter density, distribution, and cluster size — Zwicky found that the velocity dispersion of a mechanically stable Coma Cluster should be around 80km/s. This line of reasoning covered all of the system’s visible matter — so he entertained the notion that perhaps a large density of non-luminous matter might be responsible. He concludes by stating that this remains an unsolved problem.
In 1936, the dynamics of the Virgo Cluster were being studied by Sinclair Smith. Following a similar series of logical steps as Zwicky, he determined that the average mass of the galaxies in Virgo was two orders of magnitude higher than Hubble’s estimate. Galactic masses are often given in solar mass units, which relates them to the mass of our sun. This allows for easy conversion into a ratio of solar masses to solar luminosity known as mass-to-light ratios (our Sun’s is equal to one). This is important, because we generally take our sun to be a standard star, and so its ratio of mass to light should be representative of stars in general. Yet, both Zwicky and Smith were getting extraordinarily high ratios — with Zwicky’s original calculation giving a mass-to-light ratio of around 500. Even after correctly adjusting for galactic mases and a more accurate value of the Hubble parameter, both measurements still pointed to a major unsolved problem. However, the community at large still couldn’t determine if either cluster was stable, which would invalidate Zwicky’s usage of the Virial Theorem. It wasn’t until many years later that these measurements were done with adequate precision, confirming the anomalous observations of Smith and Zwicky.
In 2004, the collision of two galaxy clusters was observed. The usual dynamics of cluster collision prevailed, and it seemed that most of the galactic mass was in the form of X-rays. These X-rays interacted electromagnetically and remained in the center of the collision site. However, by observing the weak gravitational lensing of background objects, it was determined that most of the mass of the then named Bullet Cluster was actually concentrated in regions beyond the collisional X-rays. Between this measurement, the strange behavior of clusters and the non-Keplerian rotation curves, it is beyond a shadow of a doubt that our fundamental ontology is incomplete. I will now examine how this anomaly presents itself on the large scale, and begin shifting towards possible explanations.
Cosmological Abundance Constraints
Many converging lines of evidence have been taken into account when constructing our cosmic origin story. Using our known physics, and working backwards, we can derive a consistent picture of the early universe. For instance, the observation that the universe is currently expanding leads us to naturally believe that if we go far enough backwards, everything would eventually be at the same place at the same time, known as a singularity. In the same vein, as the universe gets cooler, it can be assumed that early on it was much denser and hotter.
Big Bang Nucleosynthesis
The next series of observations I want to present are the constraints placed on the amount of baryonic matter in the universe. Prior to the precise measurements of the microwave background anisotropies, big bang nucleosynthesis (BBN) was the primary means of constraining baryon density. Using spectroscopic method, astronomers found an abundance of light nucleotides such as deuterium, He3, He4 and Li7 in the cosmos. These findings conflicted with current models of stellar and supernova nucleosynthesis, given that many of these elements are not made within stars, but actually used by them as fuel. It was soon determined that approximately 25% of the baryonic matter density of the universe is helium — and there was no theoretical framework to support these observations. The work of Alpher, Bethe & Gamow in 1948 shed light on a primordial form of nucleosynthesis. They posited that an early universe form of neutron capture helped to explain the abundance of light elements. This also gave credence to the big bang view of the universe — which reports that the early universe was hot, dense and under immense pressure in its infancy. During this early period, an epoch known as baryogensis occurred, in which protons and neutrons began to form — and the asymmetry between matter and antimatter developed. As the universe continued to expand and cool, at around 10^9K, many of the light isotopes of hydrogen and helium started to form (as it was still too hot for electrons to be captured by nuclei). Since stellar observations placed limits on the abundance of light elements, and since these were formed from early baryons — the initial baryon density needed to be a carefully tuned parameter. In the 1990s Scott Burles and David Tytler released their high precision deuterium abundance measurements. These constrained baryonic abundances to 2+/- 0.2 % of the critical density to close the universe.
Acoustic Baryonic Peaks
Crucial evidence for the hot and dense big bang theory was given when Penzias and Wilson first measured the cosmic microwave background (CMB) in 1965. The CMB contains microwave photons from the very early universe. After the period of BBN, and when the universe had cooled sufficiently, the epoch of recombination occurred. Prior to this moment, the early universe was a landscape of baryon-photon plasma, oscillating inside gravitational potential wells. The early photons were created in a period of cosmic evolution in which electrons and positrons were annihilating with such frequency, that photons outnumbered baryons one billion to one. The primordial mixture of baryons, photons and electrons was opaque, as photons couldn’t travel very far without Thompson scattering off of the electrons. As the universe continued to cool, the electrons were suddenly captured by the early nuclei, allowing the photons stream unimpeded through the universe. The CMB is a snapshot of these photons moments after recombination. It initially appeared that the intensity was uniform, and this supported the view that the universe was homogenous and isotropic at large. It wasn’t until the Wilkinson Microwave Anisotropy Probe (WMAP) that small temperature anisotropies were detected. From these small-scale temperature fluctuations, scientists added more evidence to their theory of the big bang. The initial small scale spatial inhomogeneity at recombination became. These observation are reflected in the angular power spectrum of the CMB.
The first peak in this graph was the first to be precisely measured and localized. Its discovery helped to eliminate many alternative cosmological origin stories. The narrative that remained was the picture of an early universe filled with asymmetrically oscillating baryon-photon plasma. The plasma was being both compressed by gravity, and forced outwards due to the internal radiative photon pressure. The first peak represents an instance of gravitational compression — and this sonic pressure wave propagated throughout the universe. The outward photon pressure, strength of compression, and ratio of the heights of the peaks in the above graph are all highly contingent on baryon density. The measurements of the second and third peaks helped to highly constrain baryon density and the recent 2015 measurements from the Planck Collaboration have placed further constraints on baryonic matter, obtaining the highly precise density measurement of: 0.048+/-0.0005 of closure. If one subscribes to the early notion of dark matter contributing to the gravitational potential of clusters, then these new restrictions open up the possibility that the dark mass could be non-baryonic.
Large Scale Structure
The universe has a wide variety of structures: from superclusters, filaments, galactic sheets to the Great Wall and the Great Attractor. These large-scale structures were formed, in part, due to perturbations in the density of the very early universe. Small quantum vacuum fluctuations in the moments before the big bang were expanded during inflation and frozen as large scale classical fluctuations. These provided an underlying gravitational structure that attracted baryonic matter. However, before the epoch of recombination, structures were not able to form, as the universe was still too hot and dense for electron capture to occur. Given our current knowledge of the age of the universe — it appears that many of the large structures would not have had time to occur if they could only start forming after recombination.
Inference to the Best Explanation
The observations outlined thus far have some striking commonalities. At the most abstract level, they point to a breakdown of the laws of physics at both large scales of distance, and when going far back in time. Our conception of gravity stops working when we apply it to galaxies, clusters and the dynamics of the early universe. Either our formulation of gravity has to change, or there is something we can’t see contributing to the mass of the cosmos. Before moving to possible explanations, I want to briefly summarize the anomalous observations so far:
· Galaxies within clusters are moving too quickly to remain gravitationally bound
· The rotation curves of galaxies do not show a velocity drop off — galaxies far from the galactic center are moving too quickly
· The large-scale structures of the universe would not have had enough time to form given our abundance constraints on baryonic matter, and our current cosmological picture obtained from the CMB data
In short: we see the effects of gravity where normal matter is not present
The most natural solution to the problem of missing galactic mass is that there are low luminosity objects contributing to gravitational field of galaxies and clusters. These astrophysical objects are still baryonic and couple with photons, yet give off so little light that our optical devices are simply not powerful enough to pick up their signals. This line of reasoning doesn’t force us to depart from our current models, and is also helped by the fact that most of the baryons of the universe are dark and unaccounted for. Much attention was shifted to compact low luminosity objects, known colloquially as MACHOs (massive astrophysical compact halo objects). These include: planets, brown dwarfs, red dwarfs, neutron stars and black holes. A theory of intracluster gas was briefly entertained, but it was shown in 1971 that such gas would only contribute a negligible amount of mass. One of the primary cases against MACHOs is that they cannot possibly provide enough mass to account for the gravitational anomalies observed due to the baryonic abundance constraints. Summing up all the baryonic matter we can see, and given the constraints, there are not nearly enough left-over baryons to form a significant amount of matter. Light was shed on the issue of dark baryons as NASA’s Chandra X-ray Observatory recently discovered that many of them resided in webs of hot diffuse gas. The discovery of the Warm-Hot Intergalactic Medium (WHIM) provided significant evidence that MACHOs do not solve the missing mass problem.
In 1982, Mordehai Milgrom proposed that there isn’t missing mass in galaxies, instead, Newtonian dynamics breaks down below a certain value of acceleration. At large radii from a galactic center, the acceleration from gravity is so minute that we enter a new regime in which Newton’s Second law is changed from F=ma to F=(ma^2)/a0. The aptly named Modified Newtonian Dynamics (MOND) thus proposes a new fundamental constant: a0 = ∼ 1.2 × 10−10 m/(s^2) , the critical value of acceleration which, if a << a0, signifies the breakdown of normal celestial mechanics. This opened up an entire class of theories that appear to account for rotation curves without postulating the existence of unseen matter. The current iteration of this theory is known as TeVes (tensor-vector-scalar gravity) — a relativistic version of MOND. Flat rotation curves are explained by this theory yet cluster dynamics and especially the gravitational lensing occurring in the Bullet Cluster remain unaccounted for. Furthermore, the 3rd peak in the CMB angular power spectrum should be depressed and smaller than the second — yet we observe the opposite occurring. However, without any experimental evidence — MOND class theories still remain on the table as a possible explanation. MOND, in conjunction with particulate dark matter, also appears to solve the gravitational anomalies.
Non-Baryonic Dark Matter Particles
Finally, we arrive to one of the most compelling explanations. The reason that gravitational potentials are more intense than expected from visible matter is because there exists a non-baryonic particle contributing to the matter density of the universe. Such a particle is dark because it doesn’t interact with the photon, and so doesn’t experience the electromagnetic force. In fact, the only interaction it appears to have with our current Standard Model is a possible coupling to the Higgs, giving it mass. As of yet, such an exotic particle has not been detected, however it accounts for much of the observational evidence outlined earlier. If particulate dark matter existed, it would be gravitationally bound to galaxies in the form of halos. This would explain the high mass to light ratios that have plagued astronomers, as well as account for the gravitational potential required to bind both the Coma and Virgo Clusters. The distribution of non-baryonic dark matter has been calculated to be in the form of extended halos surrounding galaxies — often stretching out as far as 100kpc. This would explain the high orbital velocity of objects in the outer galactic disc of M31 — the missing force of gravity now attributed to the surrounding dark matter. The Bullet Cluster collision provides outstanding evidence for particulate dark matter. Given that the particles don’t interact electromagnetically, each galaxy’s respective halo would pass unimpeded through the others. The existence of an unknown subatomic species that only interacts gravitationally is also corroborated by our current cosmological narrative. During the early universe, both baryonic and non-baryonic matter would be attracted to the high gravitation regions. However, the dark matter wouldn’t be involved in the baryon-photon plasma, and would in fact provide an extra force during the compressions. This would translate to the odd peaks in our power spectrum being more dramatic — which is exactly what we see in our first and third peak. Non-baryonic particles would also be able to start forming structures long before the epoch of recombination, and this helps to explain the large structures that we see today. Finally, one of the strongest cases for non-baryonic dark matter are the abundance constraints placed on baryonic matter. Using the BBN and WMAP arguments, there doesn’t seem to be enough baryonic matter left to account for all of the gravitational anomalies present in our observations. Thus, particulate non-baryonic dark matter is an attractive alternative to the MOND arguments presented earlier.
We began this survey by outlining the current state of our best scientific theories. From the beginning, it was clear that a coherent and unified account of both gravity and quantum field theory had not yet been formulated. Our problems with gravity continued to manifest as a theoretical breakdown was then made increasingly clear: gravitational forces kept appearing in places where baryonic matter was not present. Further issues pertaining cosmology were then raised, from the landscape of the early universe (as determined from WMAP) and of the formation of large scale structures in the universe.
As MACHOs were systematically made implausible, the theory of a non-baryonic subatomic particle became increasingly popular. Not only does it solve all of the issues outlined in this paper, but many current candidates greatly increase the scope of our understanding. Supersymmetry provides a solution, by positing that the lightest super partner (a stable particle that all other supersymmetric counterpart particles decay into) would be both abundant and of the correct mass-energy. Another alternative is a solution to the strong CP problem, occurring in the study of the strong nuclear force known as Quantum Chromodynamics. It asserts that despite lack of observational evidence, charge-parity symmetry should be broken. This broken symmetry would imply the existence of a new boson called an Axion. Such a particle would be an ideal dark matter candidate, again, due to its calculated abundance and mass range. Weakly Interacting Massive Particles (WIMPs) are the class of particles to which a non-baryonic species belongs. As the name suggests, all of these particle candidates have mass and interact very subtly with baryons of the Standard Model. This provides unique challenges when it comes to detection attempts. Every search has thus far been plagued with sensitivity issues, and the problem of discerning signal from noise has become super salient. Since no dominant theoretical framework exists, detection attempts occur from within their respective models. The SUSY adherents search for the lightest supersymmetric particle through direct nuclei scattering events. Other experiments look for annual modulations in dark matter abundance based on where Earth is in its orbit around the Sun. Much work still needs to be done before attempting accelerator production of dark matter or indirect detection through annihilation jets. This is an exciting time in physics, as a great mystery has presented itself to us. The universe has once again forced us to reassess the state of our knowledge. While we are certain that our theories breakdown at a certain point, no clear alternative has emerged. Until then, scientists must continue to trust their patience, diligence and ingenuity.