The beautiful spinning pinwheel of the Andromeda galaxy, our celestial neighbor, poses a mystery. The breakneck speed of its rotation cannot be explained by applying the known laws of physics to the disk's visible matter. By rights, the gravity generated by the galaxy's apparent mass should cause the stars in the periphery to move more slowly than they actually do. If there were nothing more to the galaxy than the visible matter, then Andromeda—and nearly all such fast-rotating galaxies—simply should not exist.

Cosmologists believe that some unseen kind of matter surrounds and permeates Andromeda and other galaxies, adding the necessary gravitational force to keep them spinning as observed. This dark matter appears to contribute about 25 percent of the universe's mass. And it could also explain other puzzling aspects of the cosmos, from the exceedingly fast motion of galaxies within clusters of galaxies, to the distribution of matter that arises when clusters collide, to the bending of light by the gravity of distant galaxies, a phenomenon known as gravitational lensing.

The simplest theories of dark matter postulate that a single kind of particle contributes the unseen mass. But in spite of decades of searching for direct evidence of the dark matter particle, no one has been able to prove its existence. A few discrepancies also remain between astronomical observations and this simple theory.

Some scientists have begun to question the traditional, single-particle theories and to imagine a more complicat-ed form of dark matter. Perhaps, they suggest, a wide array of dark species exist. After all, ordinary matter comes in many forms—maybe dark matter is similarly complex.

Over the past few years both theoretical work and observations of colliding galaxies have lent preliminary support to the idea that dark matter comes in several varieties. Even more intriguing, these advances hint that previously unsuspected forces act strongly on dark matter and very feebly (or not at all) on ordinary matter. Such forces could help explain some of the discrepancies between the basic dark matter model and observations. If complex dark matter did exist, it would make for a more interesting and intricate universe than cosmologists usually imagine.

Hidden matter
Although we do not yet know what constitutes dark matter, we do know something about its properties from our observations of how it influences normal matter and from simulations of its gravitational effects. We know, for instance, that dark matter must be moving much slower than the speed of light. Otherwise the density fluctuations present in the early universe would not lead to the galactic structures observed today. We also know that dark matter must be electrically neutral because it does not absorb or emit electromagnetic radiation.

The particles that compose dark matter are probably massive, or else they would have to be moving near the speed of light, which data from the early universe rule out. They cannot interact via the strong force, which binds atomic nuclei together; otherwise we would have seen evidence in dark matter's interaction with high-energy charged particles called cosmic rays.

Until recently, scientists believed that dark matter might interact via the weak force (responsible for radioactive decay), but new observations have undercut that notion. If dark matter did experience weak force interactions, it appears there would have to be other undiscovered particles of regular matter as well.

Dark matter must be stable on cosmic timescales, for the simple reason that there is no credible mechanism to continually produce dark matter. The stuff thus must have originated in the primordial big bang. That in turn implies something profound: the stability of dark matter over billions of years tells us that it possesses a property that is “conserved,” meaning it cannot change. And it rules out the possibility that dark matter particles could decay because doing so would alter the conserved property.

The situation is analogous to the familiar electrical charge, which ensures that the electron is stable. It is a truism of physics that particles decay into lighter ones unless something prevents that decay. The electron is electrically charged, and the only known stable particles lighter than it are electrically neutral: the photon and the neutrinos. Energy considerations would allow the electron to decay into these objects, but because conservation of charge prohibits such decays, the electron stays an electron.

In most dark matter theories, the conserved quantity of dark particles is called parity, for historical reasons. The dark matter particle has a parity of −1; all other known particles have a parity of +1. If a dark matter particle decayed into ordinary matter, the parity would not be conserved. So the theories assume that dark particles are prohibited from decaying.

The simplest theory that meets all the conditions physicists have outlined posits a single particle responsible for dark matter. They call it a WIMP, a weakly interacting massive particle. (The term “weakly” here is used in the generic sense and does not necessarily mean the weak nuclear force.) WIMPs make sense for many theoretical reasons, but they are proving harder to find than many physicists expected.

Since the 1990s scientists have been running various experiments aimed at directly detecting WIMPs through their very rare interactions with ordinary matter. To achieve the necessary sensitivity, the detectors are cooled to extremely low temperatures. They are also buried deep underground to shield them from ubiquitous cosmic rays, which can mimic a dark matter signature. Yet despite increasingly powerful experiments, no conclusive sign of WIMPs has emerged.

Although the WIMP model does explain many aspects of our observed universe, it does not account for everything. For example, WIMP theories predict that a much greater number of small satellite galaxies should be orbiting the Milky Way than do actually appear to swirl around it. The theories also predict that dark matter should be denser in the center of galaxies than it seems to be, based on the galaxies' observed rotation rates. The situation is evolving rapidly, however. The recent discovery of additional satellite galaxies by the Dark Energy Survey collaboration suggests the problem with the Milky Way's dwarf galaxies may simply be that many have yet to be found.

Nevertheless, these WIMP shortcomings have left the door open for more unconventional dark matter models.

Complex dark matter
It could be that there is more than just one kind of dark particle. An alternative possibility is that several classes of dark matter particles exist, as well as a variety of forces that act only on them. One idea that appears to reconcile all the observations and simulations is the possibility that dark matter particles interact with one another through some force that ordinary matter cannot feel.

These particles could, for instance, carry a new kind of “dark charge” that attracts or repels them even though they are electrically neutral. Ordinary particles with electrical charge can emit photons (particles of light that are the carriers of the electromagnetic force). Perhaps dark particles have dark charge and can emit “dark photons”—not particles of light but rather particles that interact with dark charge in the same way that photons interact with electrical charge.

The parallels to the world of normal matter must end at a certain point, however. If rules of the dark world exactly mirrored ours, then dark atoms would form and emit dark photons at the same rate that ordinary matter emits ordinary photons. We know from observing the shapes of galaxies that this does not happen.

Photon emission and galaxy shape might not seem connected, but they are. It is through the emission of photons that clouds of gas inside galaxies radiate electromagnetic energy. That radiation results in the spinning matter inside the clouds clumping together and eventually relaxing into a disklike structure.

If the rules and forces governing the behavior of dark matter were the same as ours, the emission of dark photons would result in all dark matter galaxies forming flattened disks. Yet we know that the distribution of most of the dark matter required to explain our familiar galaxies is more like a spherical cloud. We can thus rule out an exact mirror world of dark matter.

Still, many alternatives remain. It is possible, for example, that a small fraction of dark matter mirrors the rules of our universe and that the remainder acts more like the simple WIMPs. Or perhaps the dark charge is effectively much smaller than the electrical charge of our electrons and protons, resulting in a far smaller amount of dark photon emission.

Theorists, including one of us (Dobrescu), are generating many ideas about possible particles and forces of the dark sector, using existing data to guide our thinking and constrain speculations. One of the simplest scenarios involves just two kinds of dark matter particles. It offers a glimpse of some of the physics that could operate in complex dark matter.

Dark photons
Imagine a dark world in which two kinds of dark charge exist—one positive and one negative. In this world, a form of dark electromagnetism allows the dark matter particles to both emit and absorb dark photons. The dark particles are charged in a way analogous to ordinary electrons and antielectrons (aka positrons). Positively and negatively charged dark matter particles should thus be able to meet and annihilate into dark photons, just as electrons and antielectrons annihilate on contact and convert their combined mass into an equivalent amount of photons.

We can make some conclusions about the strength of the dark electromagnetism force—and thus how often dark matter annihilation occurs—by considering how this force would affect galaxies. Recall that the reason galaxies have a flattened structure is that electromagnetism allows ordinary matter to lose energy and settle into disks. This energy loss occurs even without annihilation. Because we know that dark matter is primarily distributed spherically around most galaxies and does not collapse to a disk, we can conclude that it cannot lose energy via dark photon emission at the same rate that ordinary matter does.

In a study published in 2009, Lotty Ackerman, Matthew R. Buckley, Sean M. Carroll and Marc Kamionkowski, all then at the California Institute of Technology, showed that this requirement implies that the dark charge must be very small, about 1 percent of the value of the electrical charge. Yet even at such a low value, the force could still exist and have significant effects on the structure of galaxies.

Dark galaxy
So far we have described a version of dark matter consisting of a charged dark particle and its oppositely charged antiparticle emitting dark photons. But this scenario still pales in comparison to the complexity of ordinary matter. What would a dark matter world having multiple different charged particles look like?

Many theories of complex dark matter include two or more hypothetical dark particles. One particularly intriguing example was proposed in 2013 by JiJi Fan, Andrey Katz, Lisa Randall and Matthew Reece, all then at Harvard University, who referred to their model as “partially interacting dark matter.” They assumed the bulk of dark matter is made up of WIMPs. But they also postulated that a small component consists of two classes of dark fermions. (Fermions are particles—such as protons, neutrons and the quarks that compose them—that have a quantum-mechanical spin of ½.) One dark fermion in this theory is heavy and the other is light, but both carry dark charge. They both thus emit dark photons and can be attracted to each other.

The proposed situation is broadly similar to postulating a dark proton, a dark electron and a dark photon to carry the dark electromagnetism that binds them together, although one must take care to not overinterpret the correspondence. If the dark fermions had appropriate masses and charges, they could conceivably combine to create dark atoms with their own dark chemistry, dark molecules and possibly even more complex structures. This concept of dark atoms had already been explored in detail in 2010 by David E. Kaplan, Gordan Z. Krnjaic, Keith R. Rehermann and Christopher M. Wells, all then at Johns Hopkins University.

The Harvard physicists who proposed dark matter fermions went on to derive an upper limit on the fraction of dark matter that may be strongly interacting with dark photons, given the constraints imposed by astronomical observations. They determined that the total mass of such particles might equal that of all visible matter.

In this model, the Milky Way galaxy consists of a large spherical cloud of WIMP-like dark particles, which contributes 70 percent of the total matter, encircling two flattened disks, each containing 15 percent of the matter. One disk is normal matter, which includes the spiral arms that we can see, and the other consists of strongly interacting dark matter. The two disks need not be exactly aligned, but they would have a similar orientation.

In this picture, a dark matter galaxy basically coexists in the same space as our familiar Milky Way. A cautionary note: the dark matter galaxy could not include dark stars or large planets. If it did, they would have caused gravitational lensing effects on the light from ordinary matter; such effects have not been seen.

The idea may sound radical, but the extra disk in our galaxy would do little to change the normal matter cosmos with which it coexists. After all, to be correct, any theories about dark matter have to be consistent with existing observations of visible matter. We could be living in such a universe without even knowing it.

Experimental prospects
Scientists can search for complex dark matter in the same ways they search for WIMPs: by using sensitive underground detectors. One consequence of the Harvard model of partially interacting dark matter is that any of these dark fermions passing through our detectors would be denser than that predicted in WIMP models. If correct, the increased density could mean that the probability of finding dark matter with these detectors is higher than conventional theory predicts.

The search for such dark particles is under way. Physicists are also conducting experiments with particle accelerators in the hope of making dark matter, along with all the other exotic particles generated by high-energy collisions. Because we know very little about how dark matter interacts with ordinary matter—and thus which particular processes inside the accelerator might give rise to it—the program of investigation is deliberately broad. It is sensitive to models ranging from the simple WIMP to a more complex dark sector.

Of course, we must make some assumptions. If dark matter interacts only gravitationally, for example, we will never create it in any conceivable accelerator, nor will we see it in any direct search—gravity is simply too weak. So scientists assume that dark matter interacts with ordinary matter via a force or forces that are much stronger than gravity and yet weak enough to not have been observed already. This force linking dark and ordinary matter, we should note, is thought to be different from the chargelike force through which dark matter might interact with itself.

The Large Hadron Collider (LHC) at CERN near Geneva is the world's highest-energy accelerator. That gives it an edge when searching for heavier versions of dark matter, for two reasons. First, the more massive a particle is, the more energy it takes to produce it in an accelerator. Second, dark matter particles may interact more frequently as their energy rises.

We already know that dark matter can interact only very weakly with ordinary matter. So we cannot expect to observe it directly in the detector, which is made of ordinary matter. Instead scientists have been searching for dark matter by looking for collisions in which energy is missing.

For example, two protons might collide and produce some ordinary particle or particles exiting one side of the collision and a couple of dark matter particles on the other. A detector would register energy on one side but nothing on the other side. Scientists calculate how many collisions would be expected to show this striking configuration if dark matter did not exist. They then check to see whether there are more than expected.

So far no signs of such an excess have shown up inside the LHC—an indication that dark matter's interactions with ordinary matter must be very infrequent, if they occur at all. But a new opportunity for seeing signs of dark matter began in June with the start of the LHC's upgraded, higher-energy second run. That means that the discovery of the century could be right around the corner.

The searches for dark matter we have just described are suitable for finding both WIMPs and complex dark matter. But other approaches in development aim more specifically at the complex dark sector. Many of them search for the dark photon.

Some models suggest that dark photons can continually transform into ordinary photons and back again via the laws of quantum mechanics, potentially presenting an opportunity to see the photons that result. Other models suggest that certain dark “photons” have a nonzero mass (quite different from the familiar massless photon). If a dark photon has mass, it can potentially decay into lighter particles. And if a dark photon can indeed transform briefly into a normal photon, then there is a small chance that during the transformation process it can produce pairs of electrons and antielectrons (also known as positrons). Alternatively, it might create a muon (a cousin of the electron) and an antimuon.

Experimental collaborations, including a project on which one of us (Lincoln) is a member, are now monitoring accelerator collisions for the production of electron-antielectron pairs or muon-antimuon pairs. In addition to studies at the LHC, such work is ongoing as part of the KLOE-2 project at the Frascati National Laboratories at the National Institute for Nuclear Physics in Italy, the Heavy Photon Search experiment at the Thomas Jefferson National Accelerator Facility in Newport News, Va., and the BaBar detector experiment at SLAC National Accelerator Laboratory in Menlo Park, Calif. Scientists are even digging through data taken more than a decade ago by a SLAC experiment known as mQ.

Our group at Fermi National Accelerator Laboratory in Batavia, Ill., is trying to make beams of dark matter particles by shooting intense beams of neutrinos at distant detectors. Neutrinos are very light subatomic particles that interact essentially exclusively through the weak nuclear force. If dark matter interacts with ordinary matter via particles like dark photons, it is possible that dark matter is being made in the same beams and can possibly be detected in Fermilab's MiniBooNE, MINOS or NOvA detectors.

Finally, scientists can search for astronomical signs that dark matter is interacting in situations such as when galaxies collide. In such scenarios, when the dark matter from one galaxy slams into the dark matter in another, the particles could repel one another by exchanging dark photons. Several studies of galaxy crashes have failed to find evidence of this phenomenon. But recent observations of the cluster Abell 3827, which is particularly close to Earth and well oriented, hint at just such a pattern. Further observations of that and other galaxy collisions will be necessary to confirm the signal, but the data from this cluster so far look promising for complex dark matter models.

A cosmic stumper
There is no question that we are facing a profound conundrum. On large scales, ordinary gravitationally bound matter does not act in ways consistent with the known laws of physics and the observed distribution of mass. Because of this disagreement, most scientists are confident that some form of dark matter exists. What form this matter takes, however, has become increasingly contentious as our experiments repeatedly fail to find evidence for the simplest dark matter models. For this reason—and because of some persistent discrepancies between the simple WIMP model predictions and astronomical observations—theories of complex dark matter are becoming more appealing. These models offer theorists more parameters to tune and thus to improve the agreement between data and theory. They also more closely match the variation and richness of normal matter.

A criticism of this approach may be that it works overly hard to keep the dark matter hypothesis alive. Could this situation be similar to the discredited idea of epicycles, whereby 16th-century astronomers tried to save Earth's central position in the universe by continually tweaking a fatally flawed theory? We think not. Dark matter explains many astronomical conundrums remarkably well, and there is no a priori reason why dark matter should be as simple as the WIMP hypothesis.

The real message is that we have a mystery before us. We do not know what the answer will be. Until we find it, we must be open to myriad explanations, including the fascinating possibility that we might be living alongside a dark parallel reality. Could it be that a dark matter scientist has turned its attention to its skies and is wondering about us?