Dark Matter : A Literature Review

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DARK MATTER: A LITERATURE REVIEW

SOHAM PAL

1. Introduction

Dark matter is hypothesized to make up about 26% of the known universe. The rest of

the universe is supposedly composed of ordinary matter (around 5%) and the so-called dark

energy (roughly 69%).

Figure 1. Estimated distribution of matter and energy in the universe, today(top) and when the Cosmic Microwave Background was released (bottom).Source:http://map.gsfc.nasa.gov/media/080998/index.html

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http://map.gsfc.nasa.gov/media/080998/index.html





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However so far we have not been able to get direct visual evidence of dark matter. Then

why does it form such an important part of the model of the universe? Though not visible

directly, the existence of dark matter is inferred through its gravitational influence on sur-

rounding matter, on radiation and the finally by its influence on the large scale structure of the universe and this influence makes dark matter an essential ingredient in the model of

the universe.

Dark matter was originally hypothesized to account for the large discrepancy in the mass

of large scale objects as calculated from their gravitational effects and their mass as calcu-

lated from the directly observable matter that those objects contain.

Most of the current astrophysical detection methods are based on observing some kind of

electromagnetic radiation. However this fails in the case of dark matter. This is because

dark matter does not emit or absorb any kind of electromagnetic radiation at any significant

levels. But there’s reason to hope. The LIGO (Laser Interferometer Gravitational-Wave

Observatory) experiment aims to directly detect the gravitational waves predicted by Ein-

stein’s general theory of relativity. It has been theorized that gravitational collapse of dark

matter will produce gravitational waves. If the LIGO experiment detects such waves then

that would be a strong evidence in the favor of the existence of dark matter and would also

give us some knowledge about the properties of dark matter.

In this review, I will briefly discuss the history of dark matter research, give a brief overview

of the competing theories of dark matter and conclude with what could be possible future

in dark matter research.



DARK MATTER: A LITERATURE REVIEW 3

2. History of Dark Matter observation

As I stated in the previous section, so far no one on Earth has been able to observe dark

matter. However the first existence of dark matter was first postulated by the Dutch as-

tronomer Jan Oort, after whom the Oort’s Cloud is named, in 1932. While studying stellar

motions in local group of galaxies Oort noticed that the mass in the galactic plane must be

greater than what is accounted for by the visible massive objects. Oort theorized that there

must be some unseen mass in galaxies. This was the corner stone of dark matter research.

Ironically it was later shown by Kuijken and Gilmore (1989) that Oort’s measurement were

erroneous. However, for good or bad, dark matter was already a buzzword in physics re-

search by then and one of the physicists responsible for that was the Swiss astrophysicist

Fritz Zwicky.

Zwicky was studying the Coma cluster of galaxies in 1933. He used the virial theorem to

compare the cluster’s total mass based on the motions of galaxies near its edge and the total

mass based on the number of the galaxies and the total brightness of the galaxy. His calcu-

lations showed that the total mass of the cluster is about 400 times of what was accounted

for by the directly observable sources. This was the first true evidence that some unseenform of matter exists. Zwicky coined the term ‘dunkle materie’ or dark matter for this new

form of matter.

Zwicky’s calculations were not totally flawless. Modern calculations show that Zwicky’s

predictions were off by more than an order of magnitude. However his calculations were

correct enough to firmly establish the idea that there is some unseen form of matter, which

in all likelihood is very different from ordinary matter.

And then in 1939, Horace Babcock used galaxy rotation curves to show that the mass-to-

luminosity (ML) ratios of galaxies are far off from 1. A galaxy rotation curve (also called a

velocity curve) is a plot of the measured magnitude of the orbital velocities of visible stars or



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gas in that galaxy versus their radial distance from that galaxy’s center. The measurements

reported by Babcock showed that the orbital speed of stars and gas increases radially. Given

the observed mass distributions in galaxies, the orbital speed should decline at increasing

distances in the same way as it does in other systems with most of their mass at the center.This suggested that the ML ratio increases radially and is anything but 1. Though Babcock

did not attribute the discrepancy to some form of unseen matter, in hindsight it appears

that dark matter is probably the chief culprit here.

Figure 2. Rotation curve of a typical spiral galaxy. The dotted line showsthe theoretical prediction and the solid line shows the observational data.

After a couple of decades of doldrums, first ‘conclusive’ evidence in the support of dark

matter was provided in the late 1960s and early 1970s by the American astronomer Vera

Rubin and her co-worker Kent Ford. Rubin discovered that most stars in spiral galaxies orbit

at roughly the same speed. This implied that the mass densities of the galaxies were uniform

beyond the observational boundaries. Rubin’s calculations showed that most galaxies must




contain about 6 times as much unseen mass as could be accounted for by the visible sources.

Based on her work and that of others galaxies were classified into three main groups:

• Low-surface-brightness (LSB) galaxies: These are supposed to be dominated

by dark matter. One extreme example of which would be the VIRGOHI21 in the

Virgo Cluster. VIRGOHI21 has no visible stars and is considered to be made almost

entirely of dark matter. It is estimated that the VIRGOHI21 has 1000 times more

dark matter than ordinary matter.

• Spiral galaxies These have a dark matter halos which extend to distances far greater

than the visible boundaries of the galaxies. The Milky Way, our home galaxy, sup-

posedly has 10 times more dark matter than ordinary matter.

• Elliptical galaxies Many of these show evidence for high dark matter content via

strong gravitational lensing, however the situation of elliptical galaxies are not com-

pletely understood at the present.

• And then there are galaxies like the NGC3379 which show no evidence of dark matter.

3. Constituents of Dark Matter

We have a fairly complete understanding of what constitutes ordinary matter. The recent

discovery of the Higgs particle validates the Standard Model that tells us what makes up

ordinary matter. And though the standard model does not answer many question it does

give a more-or-less complete picture about the make up of ordinary matter. However we have

no such complete picture about what constitutes dark matter. There are some competing

theories and circumstantial evidences that support one theory or the other. I will discuss

these theories in this section.

Most theorists agree that dark matter is either composed of supersymmetric light (as in

less massive) particles or weakly interacting massive particles or WIMPs, that interact thor-

ough gravitational and weak forces, making them extremely hard to detect.



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Though there are many alternatives to the WIMPs/SUSY theories, only a few of them

have managed to gain some traction. Of these the most promising one is the ‘Hidden Valley’

theory which says that the dark matter exists in parallel world that is completely made up

of dark matter particles and that can only interact with the visible, ordinary matter worldvia gravity.

However most theorists agree on that dark matter is chiefly non-baryonic in origin. though

there are certain astronomical object such as massive compact halo objects (MACHO) that

may be composed of dark matter. MACHOs are baryonic, but contrary to expectation emit

little to no electromagnetic radiation, leading us to postulate that maybe they are made up

of dark matter. However such baryonic dark matter constitutes a very small portion of the

supposed amount of dark matter in the universe.

Originally neutrinos were thought to be possible dark matter particles. Neutrinos interact

very weakly with ordinary matter, making them ideal candidates for dark matter particles.

However unlike WIMPs, neutrinos are WILPs or weakly interacting light particles. Limits

imposed by the large-structure of the universe and high red-shift galaxies lead scientists to

conclude that neutrinos can only make up a very minuscule portion of dark matter.

The proposed dark matter particles can be divided into three categories based on how fast

were they moving during the early stages of the universe. The parameter used is called the

‘free streaming length’ which is the distance the particles moved before slowing down due to

the expansion of the galaxy.

• Cold Dark Matter (CDM): CDM particles have free-streaming lengths much

smaller than a protogalaxy.

• Warm Dark Matter (WDM): WDM particles have free-streaming lengths similar

to a protogalaxy. A yet-to-be-discovered variant of the neutrino, called the sterile

neutrino, is the postulated WDM candidate.




• Hot Dark Matter (HDM): HDM particles have free-streaming lengths much larger

than a protogalaxy. Neutrinos are HDM candidates.

Though there are certain modified gravity theories, such as the Scalar-Tensor-Vector Grav-

ity (STVG) that require the existence of WDM, the astrophysical evidence is overwhelmingly

in favor of CDM, that is most research now agree that dark matter is mostly cold. The pro-

posed components of dark matter are:

• Axions: These are light SUSY particles that can annihilate themselves. Though

they haven’t been detected yet, the existence of axions solves the Srong CP problem

in QCD. Also the self-annihilation can produce by-products like gamma rays and

neutrinos which we can detect and thus indirectly observe dark matter.

• WIMPs: There are currently no known particle that exhibit the property that is

expected from a WIMP, but many beyond-the-standard-model theories predict their

existence. These are the most promising dark matter candidates. There have been

claims about detecting WIMPs, but such claims have been mostly rejected.

• MACHOs: As mentioned earlier, these form the baryonic dark matter. But most

experiemnts have ruled out MACHOs as dark matter candidates.

• RAMBOs: Robust associations of massive baryonic objects. These are clustersmade of brown dwarfs or white dwarfs. Some scientists consider them to be dark

matter candidates.

Most of the current research on CDM is based on the Λ-CDM model. I will discuss this

model in greater detail in the following section.

4. Λ-CDM

Ever since Hubble, we have known that we live in an expanding universe. The Friedmann-

Lemaitre-Robertson-Walker (FLRW) metric is an exact solution of Einstein’s field equations

of general relativity that describes a homogeneous, isotropic expanding or contracting uni-

verse that may be simply connected or multiply connected. This makes the FLRW metric

a particularly good choice for the description of our universe. The Λ-CDM model assumes



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that general relativity is the correct theory of gravity on cosmological scales and uses the

FLRW metric in conjunction with the Friedmann equations and the cosmological equations

of state to describe the observational universe from the inflationary epoch to the present

and beyond. The Λ

in the name refers to the sometimes-infamous-but-mostly-famous Cos-mological Constant. The cosmological constant was originally introduced by Einstein to

describe a static universe. Later, when it was discovered that the universe is expanding, the

cosmological constant was dropped from Einstein’s field equations. However research in the

1990s showed that a positive cosmological constant is required to account for the expansion

of the universe. This led to the Λ-CDM model. The Λ-CDM model is frequently referred to

as the standard model of Big Bang cosmology, because it is the simplest model that provides

a reasonably good account of the following properties of the cosmos:

• the existence and structure of the cosmic microwave background,

• the large-scale structure in the distribution of galaxies,

• the abundances of hydrogen (including deuterium), helium, and lithium,

• the accelerating expansion of the universe observed in the light from distant galaxies

and supernovae.

The Λ-CDM model has made a number of successful predictions in recent years. The most

notable among these are

• the existence of the baryon acoustic oscillation feature, discovered in 2005 in the

predicted location,

• the statistics of weak gravitational lensing, first observed in 2000 by several teams,

• the polarization of the CMB, discovered in 2002 by DASI,

• the 2015 Plank data agree with the predictions of Λ-CDM.

However, like most theoretical models, the Λ-CDM model isn’t without its problems. The

most important problem so far is that we haven’t yet detected any dark matter particle.

Another important problem is though the Λ-CDM predictions match successfully to the

large scale observational data, small scale (sub-galaxy) predictions leave a lot to be desired.




For example the Λ-CDM predicts too many dwarf galaxies and too much dark matter in the

innermost regions of the galaxies.

But, there is ongoing research to extend and refine the Λ-CDM model to alleviate these

discrepancies with observational data. Researchers are trying to extend Λ

-CDM by addingcosmological inflation, quintessence and other elements that are current areas of speculation

and research in cosmology. Most theorists hope that like the standard model of particle

physics, the Λ-CDM model, in one form or the other, will be able to give a satisfactory

picture of the cosmos.

5. Detection of Dark Matter: Present Endeavors

Dark matter plays a very important role in the inflationary model of the universe. It is

therefore quite a matter of urgency that we detect dark matter. And fortunately quite a few

experiments are going that aim to detect dark matter, directly or indirectly.

5.1. Direct Detection. Direct detection of dark matter can be done in two ways. One by

detecting the huge number of WIMPs/axions that supposedly pass through the surface of the

earth and the other, artificially producing them in colliders. Most of the current experiments

are trying the former approach. The Axion Dark Matter eXperiment (ADMX) centered atthe University of Washington is a huge collaborative effort between researchers worldwide

to detect axions. For the detection of WIMPs we have underground laboratories at the

Stalwell mine in Australia, Soudan mine in the US, SNOLAB in Canada, Grand Sasso Na-

tional Laboratory in Italy, Canfrac Underground Laboratory in Spain, Boulby Underground

Laboratory in the UK, Deep Underground Science and Engineering Laboratory in the US

and the Particle and Astrophysical Xenon Detector in China.

5.2. Indirect Detection. The Fermi Gamma-ray Space Telescope is searching for gamma

rays produced by the decay and annihilation of Majorana WIMPs. Also there are ground

based gamma-ray telescopes which are being used for the same purpose. Also there are high

energy neutrino detectors like AMANDA, IceCube and ANTARES that are looking for high

energy neutrinos produced by the scattering of WIMPs of ordinary matter particles. And



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as I mentioned in the introduction, there’s the LIGO experiment which is trying to detect

gravitational waves that can be produced by the collapse of dark matter.

6. Alternative theories

Cold dark matter (Λ-CDM) is not the only way to resolve the observed astrophysical

discrepancies. There are competing theories that have been successful in resolving this

discrepancies to varying degrees. Here I will discuss a few of the most promising ones.

6.1. Mass in extra dimensions. This is like the ‘Hidden Valley’ model. In this multi-

dimensional theory, of all the four fundamental forces, gravity is the only one that has an

effect across all the various extra dimensions. This explains the relative weakness of thegravitational force as compared to the other forces. Dark matter could then be a candidate

that lives in the extra dimensions and interacts with ordinary matter only via gravity.

6.2. Topological defects. Dark matter could consist of primordial defects (defects origi-

nating with the birth of the universe) in the topology of quantum fields, which would contain

energy and therefore gravitate.

6.3. Modified gravity. One modified theory of gravity, the STVG proposed by John Moffat

requires the presence of WDM particles. STVG is actually a successor Mordehai Milgrom’s

Modified Newtonian Dynamics (MOND).

MOND has been successful in explaining some features of galactic structures. But the

problem with MOND is that it is non-relativistic. Moffat proposed STVG to bring MOND

in line with Einstein’s general relativity. In this regard there’s one prominent alternative to

STVG. It is TeVeS or Tensor-Vector-Scalar Gravity, proposed by Jacob Bekenstein.

Another group proposed the dark-fluid hypothesis, where dark matter and dark energy

were replaced with a single form of energy, the dark fluid.




6.4. Scale relativity. This is a combination of fractal spacetime theory and general rela-

tivity, introduced Laurent Nottale. This theory suggests that potential energy arises due to

fractality of spacetime , accounting for the mass discrepancies.

7. Conclusion

Though we haven’t yet satisfactorily detected dark matter, dark matter is one of the

chief ingredients of the simplest and most elegant model of the universe. Dark matter is

still a highly relevant field of research. Actually it’s more relevant now than ever before.

The discovery of the Higgs particle completed and validated the standard model of particle

physics, but left us with a lot of unanswered questions. Now it is the time for aggressive

research in beyond-the-standard-model domains. Dark matter is one of the most prominent

beyond-the-standard-model topics. It has got a rich history behind it with contributions

from many different fields of physics. Discovery of dark matter particles will help us to

answer many of the questions that the standard model could not and also give us a more

complete picture about the nature of gravity and of the universe that we live in. And

despite the presence of many competing theories, dark matter still provides the most simplest

explanation of the astrophysical observations, and moreover does not suffer from many of the

computational and theoretical shortcomings of the other theories. I would like to conclude by

saying that dark matter is a currently the best candidate to explain many of the astrophysical

observations and is therefore a very exciting and promising field of research.

8. References

• Planck 2013 results. 1. Overview of products and scientific results. Astronomy and

Astrophysics , vol 1303, p. 5062.

• On the Masses of Nebulae and of Clusters of Nebulae. F. Zwicky, Astrophysical

Journal , vol. 86, p. 217.

• http://home.cern/about/physics/extra-dimensions-gravitons-and-tiny-black-holes.

• An Introduction to the Science of Cosmology. D. Raine, T. Thomas IOP Publish-

ing 2001, p. 30.



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• The rotation of the Andromeda Nebula. H. Babcock Lick Observatory bulletin ,

1939, no. 498.

• Rotation of the Andromeda Nebula from a Spectroscopic Survey of Emission Regions,

Vera C. Rubin, Kent W. Ford, Jr. The Astrophysical Journal , Feb 1970, vol 159,p. 379-403.

• Mass Density Profiles of Low Surface Brightness Galaxies. W. J. G. de Blok, S.

S. McGaugh, A. Bosma, V. C. Rubin. The Astrophysical Journal Letters 2001

vol. 552 (1), p. L23-L26.

• The Intriguing Distribution of Dark Matter in Galaxies. P. Salucci; A. Borriello.

Lecture Notes in Physics . 2003 vol. 616, p. 66-77.

• The Structure and Dynamics of Luminous and Dark Matter in the Early-Type Lens

Galaxy of 0047-281 at z = 0.485. L. V. E. Koopmans, T. Treu The Astrophysical

Journal 2003, vol. 583 (2), p. 606-615.

• Analysis of a Hubble Space Telescope Search for Red Dwarfs: Limits on Baryonic

Matter in the Galactic Halo. S. D. Graff, K. Freese The Astrophysical Journal

1996, vol. 456.

• The Big Bang. Joseph Silk. San Francisco: Freeman . chap. ix, p. 182.

• Fine-scale anisotropy of the cosmic microwave background in a universe dominated

by cold dark matter. N. Vittorio, J. Silk. Astrophysical Journal, Part 2 - Letters

to the Editor vol. 285, p. L39-L43.

• Heart of Darkness: Unraveling the mysteries of the invisible universe. J. P. Ostriker,

S. Mitton. Princeton University Press 2003.

• Scale Relativity and Fractal Space-Time: A New Approach to Unifying Relativity

and Quantum Mechanics. Laurent Nottale. World Scientific p. 516.

• Detection of polarization in the cosmic microwave background using DASI. Nature

vol. 420, iss. 6917, p. 772-787.

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Dark Matter : A Literature Review