The main reason that the scientific community supports the dark matter paradigm nowadays is cosmology. Cosmology is the field of research that explores the universe as a whole and concerns with its history and evolution. Our current cosmological model, the LCDM (Lambda-Cold Dark Matter), is widely accepted by the scientific community. Dark matter, and more specifically cold dark matter, is a major part of this model. However, some major problems and wrong predictions have emerged within this model over the years. Currently, more and more cosmologists think that the current cosmological model, the well known Lambda-CDM, is on the verge of crisis.
The goal of the following review is to highlight the problems in the LCDM model that are directly connected to dark matter and also to highlight some hidden problems within the dark matter paradigm itself. The subject is presented from various perspectives in order to clarify the "big picture". We hope it would be beneficial to the first-year student as well as to the professional cosmologist.
1. So Much Evidence
There is a very strong consensus nowadays among astrophysicists that dark matter is real. Our community (as of writing these lines) is so convinced in the existence of the dark substance that there is practically no room for alternatives. The reason for this is clear: dark matter plays a significant role in different fields of astrophysics. Not only does it explain rotation curves, but it also explains the discrepancies in elliptical galaxies and galaxy clusters. Not only does it explain the power spectrum of the CMB, but it is also a necessary ingredient in cosmological simulations.
Therefore, a conversation with a community member nowadays, will be more or less the same: "The nature of dark matter, the invisible substance making up over 80% of the matter in the universe, is one of the most fundamental mysteries of modern physics" he starts. "We call it dark because it does not emit or reflect light (i.e. electromagnetic radiation). However, we can still know it's there because we observe its gravitational influence."
Diving even deeper in the conversation, we'll quickly be familiar with the main arguments in favor of the dark substance: "There are so many independent evidence for its existence.
* First, rotation curves. The very famous discrepancy in galaxy rotation curves shows that the velocities in the outer parts of galaxies are too large. The visible matter alone cannot explain these values. Adding an extra amount of matter (a dark halo) would resolve this issue.
* Then we have elliptical galaxies. In those systems we cannot produce rotation curves as in spiral galaxies. However, we can estimate their overall mass by measuring their velocity dispersion. Using this value together with the virial theorem provides an estimate for the total mass of a system. In most cases it is much larger than the observed value. In galaxy clusters, the situation is quite the same. You can estimate the total mass of a cluster by using the velocity dispersion measurements, or via the effect of gravitational lensing. In both cases you get a mass which is considerably greater than the mass of the visible components.
* More evidence lies within the CMB. The well known cosmic microwave background is very close to a perfect blackbody radiation. However, it contains very small temperature anisotropies. A sky map of anisotropies can be decomposed into an angular power spectrum. This spectrum is well fitted by our Lambda-CDM model. Of course, one of the basic ingredients of this model is the CDM - cold dark matter.
* Then you have structure formation, the field in cosmology that deals with the formation of galaxies and larger structures in the universe from small early density fluctuations. Our current understanding of this formation process assumes that the density perturbations of dark matter grew up first. The resulting gravitational potential acted as an attractive potential well for ordinary matter collapsing later, speeding up the structure formation process. The successful results of those simulations (at large scales) relies on dark matter.
You see, there are so many hints! Practically, dark matter can be seen as proven".
In this page, we'll try to convince the reader that the situation is far from being proven.
"Understanding dark matter is one of the greatest goals of modern astrophysics"
2. Dark Matter And The Scientific Method
We now understand that dark matter explains several problems in astrophysics. But how should it be regarded? As an hypothesis? A full theory? A scientific idea?
Let's start simply. If dark matter will be found (e.g. by an experiment) then it will be upgraded to a status of: existing in reality. Just in the same way as apples exist in reality. In that case, we only need to connect the observed properties of this matter with the different phenomena in astrophysics. That would be a major step forward. However, as of 2019, it hasn't been found. So, how should it be regarded today?
NFW is a theory. This theory assumes the existence of dark matter and predicts how dark halos should be distributed. It can be tested against observations repeatedly. For this reason it might be falsified (i.e. in the Popperian manner). Therefore it deserves the status of a scientific theory.
Cold Dark Matter (CDM) is a theory. This theory assumes the existence of dark matter (+ some of its properties) and predicts how structures in the universe are formed. It can be tested against observations, it might be falsified, and therefore deserves the status of a scientific theory.
But dark matter is not NFW nor CDM. Dark matter nowadays is actually the following: NFW (or one of its competitors) in the domain of rotation curves + CDM (or one of its competitors) in the domain of structure formation + another theory (or one of its competitors) in another domain and so on. Dark matter nowadays should be regarded as a "parent-theory" which encompasses several different sub-theories in several different domains of astrophysics and cosmology*.
As there are many sub-theories in each domain, if one fails, or partly fails, you can always try to use another one. Moreover, these theories contain many (too many) free parameters. If a theory fails, then a new ad-hoc parameter is immediately introduced. There is even a bigger problem: most of the sub-theories are inconsistent among themselves. When you do find a set of consistent sub-theories (e.g NFW is consistent with CDM simulations and so on), huge problems are revealed. Some of these problems are discussed in the next sections.
Here is a challenge. Try to answer the following innocent question: what should one do in order to falsify dark matter? After a few minutes of wondering the answer becomes clear. There is nothing one can do nowadays in order to falsify dark matter. If, for example, NFW turns out to be incomplete (as it cannot explain LSB galaxies) then it can always be changed or replaced by another dark sub-theory. The vague nature of dark matter always allow scientists to tweak the theories post priori. In the current situation, where the sub-theories are constantly-changing to account for every new observation, dark matter is not falsifiable. Therefore, nowadays, dark matter (as a "parent-theory") is not scientific.
3. Dark Matter Gets Better
We now understand that dark matter is not a single theory. Therefore, the popular claim that "dark matter explains many independent observations" is misleading. When exposed to such a statement, one automatically imagines a single consistent theory that explains all the various observations at once. Of course, this is not the case. As was discussed in the previous chapter, dark matter is not consistent and not a single theory.
At this point the reader might be a little bit confused. If dark matter is not a single theory but rather a set of different theories, then how did it earn its unique status from the first place? Why all these different theories that explain different discrepancies share a common parent?
The answer lies in the way science evolves. Let's take an example. When cosmologists began to run complicated simulations of the universe, they already knew that dark matter "exists". It was found in galactic rotation curves before. They added this substance to their early simulations (or analytic calculations) as extra degrees of freedom. However, this "new" dark matter has nothing to do with the rotation curves' dark matter. In the best case, the two different dark matters do not contradict each other.
This kind of processes actually happen all the time. There are many discrepancies in science. It's tempting to search for exotic solutions as they are very flexible in their nature. Take for example the Neutron Decay Anomaly, the mysterious gamma-rays in the center of the milky way, the extinction of dinosaurs, the low brightness supernovas, the detection of high energy positrons, and the so on. All of the above are real & legitimate attempts to resolve existing discrepancies in science by using dark matter. The problem is not in the legitimacy of each individual study. The problem is that it creates a loop: a process that feeds itself and strengthen the belief in dark matter, although this substance has never been found.
Take the following scenario as an example: say that one of those attempts, theory X, gains credibility and becomes a mainstream solution to discrepancy Y. In the roots of this theory one can find much freedom: what are the properties of the dark particles? What are the expected behavior of their interactions? and so on. This is inevitable, dark matter is still a speculation. In any case, this theory produces some very nice results when tested against observations. As time passes, this theory will frequently be mentioned as another evidence for dark matter...
Now we have a very unsatisfying situation. Let's say someone finds a new and elegant resolution to one of the older discrepancies; rotation curves for example. He will then be faced up in front of a bigger challenge. "What about discrepancy Y? Can it be explained? Dark matter is doing extremely well there through Theory X". These kind of processes may keep dark matter alive for decades without ever being found, while independent resolutions for the various discrepancies are emerging all the time.
4. Dark Matter In Galaxies
Dark matter as a "parent theory" can never fail. Its sub theories, however, are failing all the time. In this section, we will highlight some of the main problems in the "dark-halos regime". A comprehensive review of the subject can be found here.
First, the core-cusp problem. NFW is the most common dark halo profile used today to fit rotation curves. What is a dark halo profile? It is actually a function that tells us how the halo's mass is distributed. Using it, one can calculate the extra gravitational field produced by this dark halo. NFW is popular for a good reason: it is the outcome of CDM simulations. It tries to connect the large scale results (of numerical N-body CDM simulations) with the smaller scale regime of galaxies and rotation curves. However, NFW has a problem. It doesn't doing so well, especially in LSBs (Low Surface Brightness galaxies). Its predictions for the rotational velocities and the actual observations are very often in tension. More specifically, an NFW profile predicts a "cuspy" inner region for a dark halo (i.e. the inner density is changing fast) while observations prefer a "core-like" (approximately constant density) behavior. This is known as the core-cusp problem. Of course, a lot of attempts have emerged over the years trying to resolve this problem. But those are very specific, contain more ad hoc assumptions and more free parameters, and one cannot avoid the feeling that those were mainly created to keep the current paradigm alive. In any other situation, scientists would have been so troubled with the results that they would have question the validity of the theory. But it seems that dark matter is so emotional nowadays, so this is not the case.
Sancisi's Law. This is an important and quite general observation. The problems it creates apply to all kinds of dark halos. It states that "for any feature in the luminosity profile there is a corresponding feature in the rotation curve and vice versa". In other words, small changes in the baryonic mas distribution ("features") can be seen in the total velocity distribution, i.e. in the rotation curve. It is quite unnatural from a dark-matter perspective: the dark halo is much more dominant than the baryons. Therefore, in most of the regions, the fluctuations in the baryonic distribution should barely affect the total velocity distribution. Yet, they do. The problem in LSBs is even worse. In LSBs the dark halo is believed to be dominant in every radii. Still, the velocity distribution presents each and every "baryonic bump". It seems that somehow, the total velocity cares from small baryonic fluctuations. Prof. McGaugh, in his wonderful blog post, described this situation as "The baryonic tail wags the dark matter dog".
The predictive power of simpler models. There is some competition to dark halos in the "rotation curves regime". There are several different theories (i.e. models) that are trying to explain the observed data. Some of these theories (the new approach included) are very successful in fitting rotation curves. Obviously, good results from competing theories cannot be used as an argument against existing theory. But, if the competing theory is much simpler, still achieving better results, then the reason for this must be looked up carefully. In our case, the new approach is much simpler. From a physical point of view, it is only a transformation between frames of reference. From a mathematical point of view, it includes a simple linear term with one free parameter. It is much more simple than hypothesizing a new kind of matter, distributed by different (sometime unjustified) profiles, which consists 2-3 free parameters. Bottom line: if dark halos are real, then an explanation for this coincidence must be supplied. How a simple coordinate transformation can mimic so well the behavior of dark halo profiles?
5. Dark Matter And Cosmology
Cosmology is a very active field of research nowadays. Within this field, dark matter plays a major role. Actually, its role is so major, that several disciplines within cosmology (e.g. the CMB power spectrum, structure formation, etc) are regarded by the community as evidence for the existence of this matter. It seems impossible to remove dark matter from current cosmology without changing the model dramatically. The following conclusion, therefore, seems to be inevitable:
If dark matter does not exist then the current cosmology suffers from deep fundamental problems.
Let us try to explain why this alternative cannot be disregarded. First, time scales. Cosmological models are changing dramatically every 20-30 years or so. The last change was in 1998. Back then, cosmologists observed that the expansion of the universe is accelerating. As a result, Lambda came back to our lives, this time in the form of dark energy. The thing is that 20 years is a lot of time. Most of the professional cosmologists spent most of their career during that period of time. For them, an accelerating universe and dark energy are eternal. On the other hand, 20 years are an instant when compared to the 400 glorious years of modern science. When taking this perspective, its almost funny to hear cosmologists state that "the current Lambda-CDM model of the universe is the correct one. Some details of course, need to be resolved...". Our argument is clear: cosmology today is an evolving, unstable field of research. It's not unlikely to have a completely different model in five, ten or twenty years from now. The CMB fluctuations will be just fine...
The second issue is the discrepancies that arise in the CDM (cold dark matter) regime. Substantial part of the Lambda-CDM model deals with the small-scale results of CDM simulations. These results reveal several intrinsic discrepancies. First the Missing Satellites. CDM-simulations predict that a Milky-Way sized galaxy should contain thousands of satellite galaxies while in reality there are approximately fifty. Second, the Too-Big-to-Fail problem. It seems that the local universe contain fewer galaxies with massive dark halos than expected by the model. Third, the Satellites Plane. Observations of satellite galaxies reveal an amazing property: they are located on a single plane. This is a super interesting observation, which contradicts the random motions predicted by the simulations. A comprehensive review of the "small scale" challenges of Lambda-CDM can be found here.
The third issue is the most important one: our current model of cosmology, the famous Lambda-CDM, is on the verge of crisis. Let's start with some background. One of the cornerstones of modern cosmology is the discovery that the universe is expanding. The motion of astronomical objects, due to this expansion, is known as the Hubble flow. The parameter which describes the Hubble flow, H0, is known as the Hubble constant. It represents the current ratio between a galaxy recession velocity and its distance from us. The unfamiliar (but interested) reader will find these topics (1, 2) enlightening. In recent years, the measurements of H0 became more and more accurate. Actually, there are many different ways of measuring this quantity. Cosmologists divide them into two major classes: those relying on the late universe (direct measurements) and those based on the early universe (model-dependent measurements). Those relying on the late universe (e.g. pulsations of cepheid stars) indicate that the value of H0 is ~74 [Km/s/Mpc]. However, those relying on the early universe (e.g. the CMB temperature fluctuations) give a value of ~67.5 [Km/s/Mpc]. It's important to emphasize: the second value is not directly derived from the measurements (e.g. the CMB). It's connected to the other parameters of the cosmological model as well.
As long as the uncertainties in the measurements were large, those different values could live together. But now, that the precision (of each class) has reached ~1%, those numbers are in a clear disagreement. This is known (in recent years) as the discrepancy in H0. At a first sight it doesn't look so threatening. Yet another obstacle in the course of modern cosmology. But a more careful examination of the subject reveals the deadlock. As was summarized in this July 2019 important review: "Given the size of the discrepancy and the independence of routes seeing it, a single systematic error cannot be the explanation. After a thorough re-analysis and cross checks of multiple CMB observations (Planck, SPT, ACT etc.), it is clear that systematic errors in CMB data cannot alone explain the tension. Moreover, a suite of low redshift, different, truly independent measurements, affected by completely different possible systematics, agree with each other; it seems improbable that completely independent systematic errors affect all these measurements by shifting them all by about the same amount and in the same direction."
Their inevitable conclusion is that the current model (i.e. the Labbda-CDM) must be changed in one way or another. The current model with its current parameters leads to a discrepancy. Now, there are two different ways to handle this challenge. One is to keep Lambda-CDM almost the same but adding some "necessary patches". Concepts like "early dark energy component" and "extra self-interacting neutrinos" are already thrown to the air. Such an approach is very risky. It's an endless game of inventing new tricks that somehow keep the parameter-space in the desired region. If we keep going in these directions, we will soon find ourselves with a cosmological model as in the following photo.
"if we could only add another hall between the recombined rooms it would perfectly fit our needs"
But there is also another route. After decades of thinking within the paradigm, we need to adopt new rules, new terminology and new habits in order to make better science. In terms of terminology, for example, we must separate observations from their possible explanations. The dark energy survey is a huge survey mapping galaxies, not dark energy! Dark energy may exist in reality or may not, but in any case it's part of the theory, not of the observations. In the same manner, cuspy dark halos (predicted by simulations) were not rejected due to the observation that dark halos are cored. Those were rejected due to their disagreement with observed rotational velocities. Cored models produce better fits to these velocities. Above all, we must encourage and promote new ideas and new ways of thinking. This will be the subject of our last section.
6. The Lesson (or The Story Of Young Einstein)
As Einstein himself pointed out many times, the null results of the Michelson-Morley experiment were not the catalyst for the invention of Special Relativity. The things that really bothered him were basic principles. Or more accurately, the incompatibility of basic principles.
Take for instance the principle of relativity. It's a very accepted principle since the days of Galileo Galilei. In its original form it describes the following situation: one is located in a closed room, within a ship. There is actually no observation or experiment within this room that could reveal if the ship is stationary (relative to earth) or moving with a uniform velocity. The behavior of balls, flies, water drops and so on, will be exactly the same. It seems, therefore, that the laws of mechanics are the same when introduced relative to the earth frame or the ship frame.
In the early days of the 20th century Einstein realized that there might be a problem. Why should only the laws of mechanics be invariant? What about the other basic laws of nature, e.g. the Maxwell equations? It seems natural to assume that all the basic laws of nature takes the same form in the different frames*. However, this leads to a discrepancy. The equation for the propagation of light is a direct outcome of Maxwell's equations. It turns out that the speed of light is constant and equals to c**. Therefore, this speed must take the same value relative to the earth observer as well as relative to the moving ship. But how is it possible? How can the moving observer and the rest-frame observer measure the same speed?
At this very moment, Einstein teaches us an important lesson. Instead of ignoring the problem or making a "patch", he dives deep into the very basic definitions of space and time. He shows that the actual problem lies within the way we transform velocities. It turned out that the transformation of velocities from one frame to another was only an approximation of the real formula. By going all the way down to fundamental concepts, Einstein rescued the (apparent incompatible) basic principles. It is crucial that we adopt the same attitude when dealing with current discrepancies in cosmology. We can do more "patches", that's for sure. But we might work together, as a community, to allocate more resources and pay more attention to fundamental research, as the real progress is always there.
* As long as those inertial frames are moving in uniform motion one with respect to the others. This is the special principle of relativity, a special case of the general one.
** One needs to further assume that the the speed of light is independent of the relative motion of the source. This is known as the second postulate of Special Relativity. Of course, all the observations till now support this statement. Its value equals to 299 792 458 [m / s]