1. Introduction

There is a very strong consensus nowadays among astrophysicists that dark matter is real. Our community is so convinced in the existence of the dark substance (as of writing these lines), that practically there is no room for alternatives. The reason 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. When exposed to such arguments, one justifiably assumes that there is no need to doubt the current wisdom.

​In this article, however, we wish to offer the reader a fresh look on the dark matter paradigm. We wish to show, both from an astrophysical and a philosophical point of views, that the subject is far from being settled.

2. So Much Evidence

Let us begin by "having a conversation" with a community member (the familiar reader may skip to the next section).

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. 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 into the conversation, we'll quickly be familiar with the main arguments in favor of dark matter: 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 velocities. Adding an extra amount of matter (a dark halo) would create extra gravity, which in its turn would create larger rotational velocities.

# 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. We 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 (i.e. fluctuations). A sky map of those anisotropies can be decomposed into something that is called an angular power spectrum. This spectrum is nicely fitted by our cosmological model. Of course, one of the basic ingredients of the model is dark matter..

 

# Then you have structure formation, the field of cosmology that deals with the formation of galaxies and larger structures in the universe. 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) rely on dark matter.

You see, there are so many hints! Practically, dark matter can be seen as proven "

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"Understanding dark matter is one of the greatest goals of modern astrophysics"

3. Defining Dark Matter

We now understand that dark matter explains several problems in astrophysics. But how should it be regarded? As a hypothesis? A full theory? A scientific idea?


In the late 70’s physicists had already gathered enough data to take the discrepancy in galaxy rotation curves seriously. In short, the rotational velocities at the outskirts of galaxies were found to be higher than expected. The most natural solution to this problem was to add more matter to the models. Adding an extra amount of matter (a dark halo) creates extra gravity, which in turn creates larger rotational velocities. Therefore, back then in the 70’s, dark matter could be regarded as a kind of matter, which is unseen by observations.

However, two main processes have taken place since the 70’s. The first process is the search for dark matter candidates. Since the 70’s many suggestions have been made in order to reveal the true essence of dark matter. However, all the “regular” options for dark matter candidates (for example brown dwarfs) were ruled out. The only left options nowadays are “exotic”. That is, new kinds of matter which are not made of atoms. Therefore, dark matter should be regarded as a hypothetical kind of matter, unseen by observations.

The second process is the rapid development of cosmology. Cosmology is the field of research that explores the universe’s origin and evolution. Specifically, it deals with the evolution of large structures such as galaxies and galaxies' clusters (there is a dedicated section for cosmology below). For now, let us only mention that one of the main ingredients of the current cosmological model (the LCDM) is dark matter. As we already know, over the years there were several discrepancies and mismatches in astrophysics (e.g., in galactic rotation curves, in clusters of galaxies and so on). The development of the cosmological model was made step by step and with tight relations to those discrepancies. For example, the dark halo profiles that are used to explain the high velocities in rotation curves were inspired by cosmological simulations. This is the case for the other branches of cosmology as well.

Dark matter is so integrated within the cosmological model and its different branches that it would be fair to say that if the LCDM cosmology is disproved then dark matter becomes orphan and if dark matter is disproved then the LCDM cosmology is not relevant. As such, dark matter should be regarded nowadays as a hypothetical kind of matter, unseen by observations, with many related cosmological predictions.

4. Dark Matter and the Scientific Method

Following the definition of the previous section we realize that dark matter is not a 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. This is of course not the case. As was discussed in the previous section, dark matter is a hypothetical kind of matter fully integrated within cosmology. Cosmology, in turn, is a "parent" theory with a lot of ingredients and parameters. It does explain the various observations, but with (many) problems, post-priori fine tuning and high degree of freedom.

At this point the reader might be a little bit confused. If dark matter owes its unique status to cosmology, and cosmology was developed step by step through patches (i.e., not in a consistent way), so why did it earn its reputable status in the first place?

The answer lies in the way science evolves. Let's take an example. When cosmologists began to run complicated simulations in order to study the evolution of large-scale structures in 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 an extra degree of freedom. We now have more confidence in dark matter, since it plays a significant role in another field of research.

These kinds 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 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 strengthens 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 behaviors 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. She 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 kinds 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.

Dark matter saves science

5. Dark Matter in Galaxies

In this section, we wish to highlight some of the main problems in the "dark-halos regime". That is, the branch of cosmology that deals with galactic scales.

​# 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 dark-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 Cold Dark Matter (CDM) simulations. It tries to connect the large scale results (of numerical N-body simulations) with the smaller scale regime of galaxies and rotation curves. However, NFW has a problem. It doesn't do 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.

 # 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 mass 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 radius. 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 if "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, the nice results of the competing theories cannot be used as an argument against the existing theory. But, if a competing theory is much simpler, still achieving better results, then the reason for the coincidence should be looked up carefully. In our example, the new approach is simpler. From a physical point of view, it only requires a transformation between frames of reference (and does not require hypothesizing a new kind of matter). From a mathematical point of view, it includes one free parameter while dark-halo profiles usually use 2-3 free parameters. If dark halos are real, then an explanation must be supplied: How can a simple coordinate transformation mimic so well the behavior of complicated, fine-tuned dark halo profiles? 

6. 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 significant that several disciplines within cosmology that are "purely" cosmological (e.g. the CMB power spectrum) are regarded by the community as evidence for the existence of dark matter - although they rely on dark matter only indirectly, through the LCDM model. In this section, we wish to highlight some of the difficulties within the cosmological model, specifically those that are closely related to dark matter. But 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. Twenty years is a long time. Most of the professional cosmologists spent most of their career during this period of time. For them, an accelerating universe and dark energy are eternal. On the other hand, twenty years are no more than a blink of an eye when compared to the 400 (glorious) years of modern science. When taking this perspective it's not hard to imagine a different cosmology in a few years. Actually, it is 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.

Now to 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. 1. 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. 2. The Too-Big-to-Fail problem. It seems that the local universe contains fewer galaxies with massive dark halos than expected by the model. 3. The Satellites Plane. Observations of satellite galaxies reveal an amazing property: they are located on a single plane. This is a very interesting observation, which contradicts the random motions predicted by the simulations. Comprehensive reviews of the "small scale" challenges of Lambda-CDM can be found here and here.

​The following issue is even more important: our current model of cosmology, the famous Lambda-CDM, is on the verge of crisis. Here is 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's recession velocity and its distance from us. The unfamiliar (but interested) reader will find these topics (12) 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 relies on the validity 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. As was summarized in this July 2019 workshop 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…

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COSMOLOGY

2030

"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 is 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! Above all, we must encourage and be open-minded to new ideas. This will be the subject of our last section.



The article was written before the launch of the James Webb Telescope. Webb's results create new & severe difficulties to the LCDM cosmology. A nice review of the subject, from October 2022, can be found here.

7. The Story of Young Einstein

As Einstein himself pointed out many times, the null results of the Michelson-Morley experiment were not the catalysts 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 has been very accepted in science 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. It turns out that no observation or experiment within the room can reveal whether 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 take 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 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] 

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“Blind belief in authority is the greatest enemy of truth”