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MOND and Other Theories on Dark Matter and Dark Energy

Dark matter theories

Dark matter theories

The Prevailing Theory

The most common viewpoint on dark matter is that it is made of WIMPS, or Weakly Interacting Massive Particles. These particles can pass through normal matter (known as baryonic), move at a slow rate, are generally unaffected by forms of electromagnetic radiation, and can clump together easily. Andrey Kravtsov has a simulator that concurs with this viewpoint and also shows that it helps clusters of galaxies stay together despite the expansion of the universe, something that Fritz Zwicky postulated about over 70 years ago after his own observations on galaxies noticed this peculiarity. The simulator also helps explain small galaxies, for dark matter allows the clusters of galaxies to remain in close proximity and cannibalize on each other, leaving small corpses behind. Furthermore, dark matter also explains the spin of galaxies. Stars on the outside spin as fast as stars near the core, a violation of rotational mechanics because those stars should be flung away from the galaxy based on their velocity. Dark matter helps explain this by having the stars contained within this strange material and preventing them from departing our galaxy. It all boils down to that without dark matter, galaxies would not be possible (Berman 36).

As for dark energy, that is still a great mystery. We have little idea as to what it is, but we do know that it operates on a grand scale by accelerating the expansion of the universe. It also seems to account for almost ¾ of all that the universe is made of. Despite all this mystery, several theories are hoping to sort it out.

Mordehai Milgrom

Mordehai Milgrom

MOND, or Modified Newtonian Dynamics

This theory has its roots in Mordelai Milgrom, who, while on sabbatical, went to Princeton in 1979. While there, he noted that the scientists were working on solving the galaxy rotation curve problem. This refers to the before-mentioned properties of galaxies where the outer stars rotate as fast as the inner stars. Plot the speed versus distance on a graph; instead of a curve, it flattens out, hence the curve problem. Milgrom tested many solutions before finally taking a list of the galaxy and solar system properties and comparing them. He did this because Newton's gravity works great for the solar system, and he wanted to extend it to galaxies (Frank 34-5, Nadis 40).

He then noticed that the distance was the biggest change between the two of them and began to think about that on a cosmic scale. Gravity is a weak force, but relativity is applied where gravity is strong. Gravity depends on distance, and distances weaken gravity, so if it behaves differently on larger scales, something needs to reflect this. In fact, when the gravitational acceleration became less than 10 -10 meters per second (100 billion times less than Earth's), Newton's gravity wouldn't work as well as relativity's, so something needed to be adjusted. He modified Newton's second law to reflect these changes to gravity so that the law becomes F = ma2/ao, where that denominator term is the rate it takes you to accelerate to the speed of light, which should take you the lifetime of the universe. Apply this equation to the graph, and it fits the curve perfectly (Frank 35, Nadis 40-1, Hossenfelder 40).

Graph showing traditional Newtonian vs. MOND

Graph showing traditional Newtonian vs. MOND

He began to do the hard work in 1981 alone because no one felt this was a viable option. In 1983 he publishes all three of his papers in the Astrophysical Journal with no response. Stacy McGaugh, from Case Western University in Cleveland, did find a case where MOND did predict results correctly. She wondered about how MOND worked on "low surface brightness galaxies," which had low star concentrations and were shaped like a spiral galaxy. They have weak gravity and are spread out, a good test for MOND. And it did great. However, scientists generally shy away from MOND still. The biggest complaint was that Milgrom had no reason why it was right, only that it fit the data (Frank 34, 36-7, Nadis 42, Hossenfelder 40, 43).

Dark matter, on the other hand, attempts to do both. Also, dark matter began to explain other phenomena better than MOND even though MOND still explains the curve problem better. Recent work by a partner of Milgrom, Jacob Bekenstein (Hebrew University in Jerusalem), attempts to explain all that dark matter does as he accounts for Einstein's relativity and MOND (which only revises Newtonian gravity - a force - instead of relativity). Bekenstein's theory is called TeVeS (for tensor, vector, and scalar). The 2004 work takes into account gravitational lensing and other consequences of relativity. Whether it takes off remains to be seen. Another problem is how MOND fails for not only galaxy clusters but also for the large-scale universe. It can be off by as much as 100%. Another issue is MOND's incompatibility with particle physics (Ibid).

Some recent work has been promising, however. In 2009, Milgrom himself revised MOND to include relativity, separate from TeVeS. Though the theory still lacks a why, it does better explain those large-scale discrepancies. And recently, the Pan Andromeda Archaeological Survey (PANDA) looked at Andromeda and found a dwarf galaxy with weird star velocities. A study published in The Astrophysical Journal by Stacy McGaugh found that revised MOND got 9/10 of those correct (Nadis 43, Scoles).

The Collision

However, a huge blow was dealt to MOND on August 17, 2017, when GW 170817 was detected. A gravity wave event generated by a neutron star collision was heavily documented in many wavelengths, and most striking was the difference in times between gravity waves and visual waves - just 1.7 seconds. After travelling 130 million light-years, the two nearly arrived at the same time. But if MOND is right, then that difference should have been more like three years instead (Lee "Colliding").

The Scalar Field

According to Robert Scherrer of Vanderbilt University in Tennessee, dark energy and dark matter are actually a part of the same energy field known as the scalar field. Both are just different manifestations of it, depending on what aspect you are examining. In a series of equations he derived, different solutions present themselves depending on the time frame we solve for. Whenever density decreases, volume increases according to his work, much like how dark matter operates. Then as time progresses, density remains at a constant as volume increases, much like how dark energy works. Thus, in the early universe, dark matter was more plentiful than dark energy, but as time goes on, dark matter will approach 0 with regards to dark energy, and the universe will accelerate its expansion even further. This is consistent with the prevailing viewpoints on cosmology (Svital 11).

A visualization of a scalar field

A visualization of a scalar field

John Barrows and Douglas J. Shaw also worked on a field theory, though theirs originated by noticing some interesting coincidences. When evidence for dark energy was found in 1998, it gave a cosmological constant (the anti-gravity value based on Einstein's field equations) of Λ = 1.7 * 10-121 Planck units, which happened to be almost 10121 times larger than the "natural vacuum energy of the universe." It also happened to be close to 10-120 Planck units, which would have prevented galaxies from forming. Finally, it was also noted that Λ is almost equal to 1/tu2 where tu is the "present expansion age of the universe," which is about 8 * 1060 Planck time units. Barrows and Shaw were able to show that if Λ is not a fixed number but a field, then Λ can have many values and thus, dark energy could operate differently at different times. They were also able to show that the relation between Λ and tu is a natural result of the field because it represents the light of the past and so would be a carry-through from the expansion of today. Even better, their work gives scientists a way to predict the curvature of space-time at any point in the Universe's history (Barrows 1,2,4).

The Acceleron Field

Neal Weiner of the University of Washington thinks dark energy is linked to neutrinos, small particles with little to possibly no mass that can pass through normal matter easily. In what he calls an “acceleron field,” neutrinos are linked together. When the neutrinos move away from each other, it creates tension much like a string. As the distance between neutrinos increases, so does the tension. We observe this as dark energy, according to him (Svital 11).

Sterile Neutrinos

While we are on the topic of neutrinos, a special type of them may exist. Called sterile neutrinos, each would be very weakly interacting with matter, incredibly light, would be its own antiparticle and could hide from detection unless they annihilate each other. Work from researchers at Johannes Gutenberg University Mainz shows that given the right conditions, these could be plentiful in the Universe and would explain the observations we have seen. Some evidence for their existence was even found in 2014 when spectroscopy of galaxies found an X-ray spectral line containing energy that could not be accounted for unless something hidden was happening. The team was able to show that if two of these neutrinos interacted, that would match the X-ray output spotted from those galaxies (Giegerich "Cosmic").

The Josephson Junction

The Josephson Junction

Josephson Junctions

A property of quantum theory known as vacuum fluctuations could also be an explanation for dark energy. It is a phenomenon where particles pop in and out of existence in a vacuum. Somehow, the energy that causes this disappears from the net system, and it is hypothesized that that energy is, in fact, dark energy. To test this, scientists can use the Casimir effect, where two parallel plates are attracted to each other because of the vacuum fluctuations between them. By studying the energy densities of the fluctuations and comparing them with the expected dark energy densities. The test bed will be a Josephson junction, which is an electronic device having a layer of insulation squeezed between parallel superconductors. To find all the energies generated, they will have to look over all frequencies, for energy is proportional to frequency. The lower frequencies so far support the idea, but higher frequencies will need to be tested before anything firm can be said of it (Phillip 126).

Emergent Advantages

Something that takes existing work and rethinks it is emergent gravity, a theory developed by Erik Verlinde. To best think of it, consider how temperature is a measure of the kinetic motion of particles. Likewise, gravity is a consequence of another mechanism, possible quantum in nature. Verlinde looked at de Sitter space, which comes with a positive cosmological constant, unlike anti de Sitter space (which has a negative cosmological constant). Why the switch? Convenience. It allows for direct mapping of quantum properties by gravitational features in a set volume. So, like in math, if given x, you can find y, you can also find x if given y. Emergent gravity shows how given a quantum description of a volume, you can get a gravitational viewpoint as well. Entropy is frequently a common quantum descriptor, and in anti de Sitter space, you can find the entropy of a sphere so long as it is in the lowest energetic state possible. For a de Sitter, it would be a higher energy state than anti de Sitter, and so by applying relativity to this higher state, we still get the field equations we are used to and a new term, the emergent gravity. It shows how entropy affects and is affected by matter, and the math seems to point to properties of dark matter over long spans of time. Entanglement properties with information correlate to the thermal and entropy implications, and matter interrupts this process which leads to us seeing the emergent gravity as dark energy reacts elastically. So wait, isn't this just an extra cute math trick like MOND? Nope, according to Verlinde, because it isn't a "because it works" but that it has a theoretical underpinning to it. However, MOND still works better than emergent gravity when predicting those star speeds, and that may be because emergent gravity relies on spherical symmetry, which isn't the case for galaxies. But a test of the theory done by Dutch astronomers applied Verlinde's work to 30,000 galaxies, and the gravitational lensing seen in them was better predicted by Verlinde's work than by conventional dark matter (Lee "Emergent," Kruger, Wolchover, Skibba).

A superfluid?

A superfluid?


Scientists have noticed that dark matter seems to act differently depending on the scale one looks at. It holds galaxies and galactic clusters together, but the WIMP model does not work well for individual galaxies. But if dark matter were able to change states at different scales, then maybe it could work. We need something that acts like a dark matter-MOND hybrid. Around galaxies, where the temperatures are cool, dark matter may be a superfluid, which has next to no viscosity courtesy of quantum effects. But at the cluster level, conditions are not right for a superfluid, so it reverts back to the dark matter we expect. And models show it not only acts as theorized but could also lead to new forces created by phonons ("sound waves in the superfluid itself"). To accomplish this, though, the superfluid needs to be compact and at very low temperatures. Gravitational fields (which would result from the superfluid interacting with normal matter) around galaxies would help with the compaction, and space already has low temperatures. But at the cluster level, not enough gravity exists to squeeze stuff together. Evidence is scarce so far, though. Vortexes predicted to be seen haven't. Galactic collisions, which are slowed down by the dark matter halos passing by each other. If a superfluid, the collisions should proceed faster than expected. This superfluid concept is all according to work by Justin Khoury (University of Pennsylvania) in 2015 (Ouellette, Hossenfelder 43).


It may seem crazy, but could the humble photon be a contributor to dark matter? According to work by Dmitri Ryutov, Dmitry Budker, and Victor Flambaum, it's possible but only if a condition from the Maxwell-Proca equations is true. It could give photons the ability to generate additional centripetal forces via "electromagnetic stresses in a galaxy." With the right photon mass, it could be enough to contribute to the rotational discrepancies scientists have spotted (but isn't enough to fully explain it away) (Giegerich "Physicists").

Rogue Planets, Brown Dwarfs, and Black Holes

Most people don't consider objects that are just hard to find in the first place, like rogue planets, brown dwarfs, and black holes. Why so hard? Because they only reflect light and do not emit it. Once out in the void, they would be practically invisible. So if enough of them are out there, could their collective mass account for dark matter? In short, no. Mario Perez, a NASA scientist, went over the math and found that even if models for rogue planets and brown dwarfs were favorable, it wouldn't even come close. And after researchers looked into primordial black holes (which are miniature versions formed in the early universe) using the Kepler Space Telescope, none were found that were between 5-80% of the mass of the moon. Still, theory does hold that primordial black holes as small as 0.0001 percent of the moon's mass could exist, but it is unlikely. Even more of a blow is the idea that gravity is inversely proportional to the distance between objects. Even if a lot of those objects were out there, they are just too far apart to have a discernible influence (Perez, Choi).

Enduring Mysteries

Questions remain about dark matter that all these attempt to solve but so far are unable to. Recent findings by LUX, XENON1T, XENON100, and LHC (all potential dark matter detectors) have all lowered the limits on potential candidates and theories. We need our theory to be able to account for a less reactive material than thought before, some likely new force carriers unseen so far, and possibly introduce a brand new field of physics. Dark matter to normal (baryonic) matter ratios is roughly the same across the cosmos, which is extremely odd considering all the galactic mergers, cannibalism, age of the Universe, and orientations across space. Low surface brightness galaxies, which shouldn't have much dark matter because of the low matter count, instead display the rotation rate problem that sparked MOND in the first place. It is possible to have current dark matter models account for this, including a stellar feedback process (via supernovas, stellar wind, radiation pressure, etc), forcing matter out but retaining its dark matter. However, it would require this process to occur at unheard-of rates to account for the amount of matter missing. Other issues include a lack of dense galactic cores, too many dwarf galaxies, and satellite galaxies. No wonder so many new options that are alternates to dark matter are out there (Hossenfelder 40-2).

The Beginning

Rest assured that these just scratch the surface of all the current theories about dark matter and dark energy. Scientists continue to gather data and even offer up revisions to our understandings of the Big Bang and gravity in an effort to solve this cosmological conundrum. Observations from the cosmic microwave background and particle accelerators will lead us ever closer to a solution. The mystery is far from over.

Works Cited

Ball, Phillip. "Scepticism Greets Pitch to Detect Dark Energy in the Lab." Nature 430 (2004): 126. Print.

Barrows, John D, Douglas J. Shaw. "The Value of the Cosmological Constant” arXiv:1105.3105

Berman, Bob. "Meet the Dark Universe.” Discover Oct. 2004: 36. Print.

Choi, Charles Q. "Is Dark Matter Made Of Tiny Black Holes?" Huffington Post, 14 Nov. 2013. Web. 25 Mar. 2016.

Frank, Adam. "Gravity's Gadfly." Discover Aug. 2006. 34-7. Print

Giegerich, Petra. "Cosmic x-rays may provide clues to the nature of dark matter." innovations report, 09 Feb. 2018. Web. 14 Mar. 2019.

---. "Physicists analyze the rotational dynamics of galaxies and the influence of the mass of the photon." innovations report, 05 Mar. 2019. Web. 05 Apr. 2019.

Hossenfelder, Sabine. "Is Dark Matter Real?" Scientific American. Aug. 2018. Print. 40-3.

Kruger, Tyler. "The Case Against Dark Matter. Kalmbach Publishing Co., 07 May 2018. Web. 10 Aug. 2018.

Lee, Chris. "Colliding Neutron Stars Apply Kiss of Death to Theories of Gravity." Kalmbach Publishing Co., 25 Oct. 2017. Web. 11 Dec. 2017.

---. "Diving Seep into the World of Emergent Gravity." Kalmbach Publishing Co., 22 May 2017. Web. 10 Nov. 2017.

Nadis, Frank. "Dark Matter Deniers." Discover Aug. 2015: 40-3: Print.

Ouellette, Jennifer. "Dark Matter Recipe Calls for One Part Superfluid." Quanta, 13 Jun. 2017. Web. 20 Nov. 2017.

Perez, Mario. "Could Dark Matter Be...?" Astronomy Aug. 2012: 51. Print.

Scoles, Sarah. "Alternate Theory of Gravity Predicts Dwarf Galaxy." Astronomy Nov. 2013: 19. Print.

Skibba, Ramin. "Researchers Check Space-Time to see if It's Made of Quantum Bits." Quanta, 21 Jun. 2017. Web. 27 Sept. 2018.

Svital, Kathy A.. "Darkness Demystified.” Discover Oct. 2004: 11. Print.

Wolchover, Natalie. "The Case Against Dark Matter." Quanta, 29 Nov. 2016. Web. 27 Sept. 2018.

© 2013 Leonard Kelley


Leonard Kelley (author) on July 31, 2019:

Thanks Tim. Glad you liked it!

Tim Truzy from U.S.A. on July 30, 2019:

Excellent article. Superbly explained with good resources. Thank you.

mpc755 on September 28, 2018:

Dark matter is a supersolid that fills 'empty' space, strongly interacts with ordinary matter and is displaced by ordinary matter. What is referred to geometrically as curved spacetime physically exists in nature as the state of displacement of the supersolid dark matter. The state of displacement of the supersolid dark matter is gravity.

The supersolid dark matter displaced by a galaxy pushes back, causing the stars in the outer arms of the galaxy to orbit the galactic center at the rate in which they do.

Displaced supersolid dark matter is curved spacetime.

Joe Bakhos on May 01, 2018:

I think that at a certain galactic distance, gravity reverses and the galaxies begin pushing against each other. This would do away with cosmological expansion, dark matter, and dark energy. This is a claim that can be easily tested:

A revised gravity equation looks like this (I have made an adjustment compared to my last version):

F = (1.047 X 10^-17) m1m2 [-cos(Θ)] / r^2 where tan Θ = r / (1.419 X 10^22)

By playing with the constants, this equation can be fitted and tested against the data of galactic motion. It means that at a certain distance, gravity will reverse and the galaxies will be pushing against each other. This pressure against each other does away with the need for dark matter or dark energy in cosmology.

So the equation can be tested against current data to see if it fits. This equation also predicts that galaxies near the edge of the universe will be deformed -- concave with the concavity pointing towards the center of the universe.

This equation also predicts the existence of isolated galaxies that are far away from other galaxies, that would behave normally without the need to posit dark matter. An example of this type of galaxy is NGC1052–DF2 . Talked about in this article:

Test this equation to see if slight adjustment of the constants will account for galactic motion or not. If it does, then proceed to the rest of the theory.

If it cannot, then the theory can be dismissed. Either way, I would like to know -- but I would not be convinced with a simple "absurd!" or dismissal unless it has been tested out.

If it is true that the motion of galaxies can be modeled in this way, I would ask that you take a look at the explanation in this theory:

Leonard Kelley (author) on January 21, 2013:

sparkster, several people have wondered about the connection between "negative energy" and dark energy. I recommend reading Physics of the Impossible by Michio Kako for more about the science behind it.

Reynold Jay, I am glad to hear from a science teacher that this post is good. Good luck on any theory you start to work on!

Reynold Jay from Saginaw, Michigan on January 21, 2013:

I'll need to look into this and come up with a theory too! Just kidd'n. Heck I was a scince teacher however my students never got to this point. Well done UP and awesome to even think of all this theory.

Marc Hubs from United Kingdom on January 21, 2013:

I don't have a particularly scientific mind but I am very interested in this kind of thing. I have previously written about "the neutrino universe" after watching a discussion with Senior Research Scientist for Lockheed Skunkwords Boyd Bushman.

So, if this dark matter is responsible for the expansion of the universe can it then be used for anti-gravity propulsion? And is it the same as zero-point energy?

Here is quote I found at NASA:

Zero Point Energy (ZPE), or vacuum fluctuation energy are terms used to describe the random electromagnetic oscillations that are left in a vacuum after all other energy has been removed. If you remove all the energy from a space, take out all the matter, all the heat, all the light... everything -- you will find that there is still some energy left. One way to explain this is from the uncertainty principle from quantum physics that implies that it is impossible to have an absolutely zero energy condition.

For light waves in space, the same condition holds. For every possible color of light, that includes the ones we can’t see, there is a non-zero amount of that light. Add up the energy for all those different frequencies of light and the amount of energy in a given space is enormous, even mind boggling, ranging from 10^36 to 10^70 Joules/m3.

In simplistic terms it has been said that there is enough energy in the volume the size of a coffee cup to boil away Earth’s oceans. - that’s one strong cup of coffee! For a while a lot of physics thought that concept was too hard to swallow. This vacuum energy is more widely accepted today.

What evidence shows that it exists?

First predicted in 1948, the vacuum energy has been linked to a number of experimental observations. Examples include the Casimir effect, Van der Waal forces, the Lamb-Retherford Shift, explanations of the Planck blackbody radiation spectrum, the stability of the ground state of the hydrogen atom from radiative collapse, and the effect of cavities to inhibit or enhance the spontaneous emission from excited atoms."