“It’s very difficult to make large scale structure if you don’t have dark matter”  - Joseph Silk[i] Astronomers have long been aware that the universe contains a lot more than can be seen from earth.  This ‘missing matter’ makes itself known in several ways, and discovering its nature is the key to solving many outstanding issues in astronomy.  Whilst some of this matter takes the form of familiar objects that elude detection through the enormous distances of space and the limitations of current technology, there is compelling evidence for a class (or classes) of matter that differ from the ‘normal’ matter that astronomers deal with.  The nature of this ‘exotic dark matter’, the evidence for its existence, and its implications on the structure and nature of the universe will form the basis of this report.

At the heart of the issue of dark matter is the light to mass (LM) ratio of various structures within the universe (and the universe itself).  Energy within the universe manifests itself as electro-magnetic radiation, across a broad range of spectra (frequencies) that is dependant upon the object emitting the radiation (and any subsequent influences prior to being detected from earth).  Whilst visible light is the most familiar form of electro-magnetic radiation (EMR),  all forms of EMR must be considered when examining the light content of an object or structure. When all visible mass is totaled, we can get an estimate for the mass of large scale phenomenon.  In the case of the Milky Way, the estimated mass based on observed matter (primarily stars, dust and hydrogen gas – H gas emits a spectra that can be detected as radio wavelengths, likewise, dust is heated by stars and emits radiation in the infrared spectrum) is 10¹¹ solar masses[ii].  This process can be applied to other structures, such as other galaxies, galactic super clusters and the universe itself. The mass of a structure has important implications for component objects (such as stars in a galaxy) or companion objects (galaxies in a cluster), because all objects interact via gravitation.  Gravitation is a very weak force, but operates over large distances.  Newton’s laws of gravity identifies that all objects are gravitationally attracted to one and other, with a force that is proportional to the mass of the two objects, and inversely proportional to the square of the distance between the two objects: $latex G \approx\frac{M_{1}M_{2}}{d^{2}}&bg=000000&fg=ffffff&s=2$ [iii]. Because gravity is proportional to mass, if we know the distance between two objects, and their velocity and direction, we can determine the combined mass of the two objects.  Modern astronomy can determine velocity via examining Doppler shifts in the spectra of EMR emitting objects.  Applying this relationship to the observations of the universe, we find that there is a vast and varying discrepancy between the amount of matter observed, and the amount of matter inferred by gravitational observations.  All evidence for dark matter is based on such gravitational discrepancies.

Evidence for Dark Matter

The history and detail of evidence for dark matter could form the basis of an entire report, so a summary of the key contributions to this field will be given.  It is important to note that dark matter manifests itself in a number of phenomenon, and leads to several ‘dark matter problems’, which may have several different solutions. A very early example (1846) of the dark matter phenomenon (and one of the few with a definite solution) was the discovery of the planet Neptune, whose existence and location were predicted by analysis of the orbit of Uranus, which showed the gravitational influence of an unknown object.  In the context of current thinking on dark matter, studies of distribution (Kapetyn and Jeans) and velocity (Oort) of stars above and below the galactic plane in the Milky Way indicated a greater gravitational mass of the Milky Way than could be explained by observation.  Oort suggested 50% of mass was missing, concluding "light is not always a reliable trace of matter."[iv]. Most objects and systems in the universe rotate (otherwise they would quickly collapse due to gravity).  As discussed, this rotation can be measured and used to determine the overall mass of the system.  Applied at a galactic level, it allows the mass of galaxies to be approximated.  Work by Babcock in the 1930’s and 40’s with galaxy M31 and Patterson (M33) attempted to measure the velocity of matter in these galaxies at various distances from the galactic centre (termed a rotational curve).  Whilst pioneering, this work relied on estimates of the distances of these galaxies (mass estimates of visible matter are related to distance which is a function of brightness), which were less accurate at this time.  Babcock assumed a distance to M31 of 210 Kpc, about a third of the current estimate of 700 Kpc (roughly 2.25 thousand light years).  Thus, mass was underestimated, and a ML ratio of 50 was arrived at (compared to current estimates of 14[v]). Extending this work, Rubin and Ford in the 1960’s studied the rotational curve of M31, using neutral hydrogen radiation lines[vi].  This detailed study showed a levelling off of the velocity curve – meaning that rather than matter slowing down the further it is from the galactic centre, as predicted by Kepler’s 3^rd law (and general Newtonian physics), it remained steady (see figure.1).  An object further from the centre has less gravitational interaction with the centre, and thus requires less speed to overcome gravity to maintain an orbit.  Only if more mass is present at these distances (a more massive centre does not solve this problem), can these objects be prevented from breaking the gravitational attraction the centre.  As such mass cannot be seen, it is a key indicator of missing mass.  Simulations by Ostriker and Peebles in 1973 showed that galaxies without dark matter in their halos induced eccentric orbits and even star ejection, which is at odds with observations[vii]. Figure 1 – Rotational Curve of M31[viii] Figure 1 also shows the existence of mass beyond the visible disc of the galaxy, an area termed the galactic halo. Studies of M87 (a particularly large galaxy) show traces of x-ray emissions from hydrogen gas.  X-rays are particularly high energy waves, and in this instance are believed to be emitted by in-falling hydrogen gas.  To achieve the velocities required, and prevent dispersion of this gas, M87 is believed to be up to 90% dark matter.  At the other end of the spectrum, dwarf galaxies are tiny galaxies with low star densities and lack a central core.  They often exist close to large galaxies (the Milky way has seven companion dwarfs).  Their existence and kinematics require masses far greater than those visible, and have ML ratios of 5 to over 100[ix]. Beyond individual galaxies, clusters of galaxies and clusters of clusters - super clusters -  all display gravitational interactions that far exceed that predicted by their visible mass.    In the case of clusters, M/L ratios may be 50-400, whilst for super clusters, 100-1000[x].  Large scale cosmic structures, essentially the big picture of the sky, show a number of patterns, including filaments (clusters following lines) and voids (areas of low cluster density), which most likely require gravitational forces to create.  Further, there are the indications of matter where no light evidence exists.  The Great Attractor, an area within a void that is attracting surrounding galaxies[xi], is such an example. Finally, when the universe is examined as a whole, there are implications for the amount of matter in the universe.  The key issue is the effect of the mass of the universe on its future.  Big bang theory produces an expanding universe, which would be slowed down by the gravitational effect of its mass.  If the universe has enough matter, the universe will eventually stop expanding, albeit over an infinite amount of time.  This situation is known as a flat universe, and there are strong theoretical reasons to support this proposition (which will be discussed later).  The ratio of the mass of the universe to that required to make a flat universe is called Ω, with Ω=1 being a flat universe. One leading prediction puts the quantity of matter in the universe (Ω_M) as 0.4Ω, with the baryonic component (Ω_B) at 0.05Ω[xii].  To achieve flatness, the of 0.6Ω is assigned to vacuum energy, a concept that will be discussed further on. In summary, the dark matter problem can be divided into three main areas:

• galactic kinematics – star motion, rotational curves and dwarf galaxies
• cluster and super cluster motions, and general cosmological structure
• cosmological expansion and unity

Dark matter Solutions

Baryonic solutions

Baryons are a class of particles that constitute the majority of the mass that is familiar to us, and primarily refers to protons and neutrons.  Electrons are actually members of the lepton class of particles, but their mass is very small compared to that of protons and neutrons, so baryonic matter is a suitable description of matter made of regular atoms. Baryonic solutions to the dark matter problem ascribe the missing matter to objects made of regular matter, but which cannot be detected by astronomers.  There are a number of candidate objects for baryonic solutions, all of which are known to exist.  It is important to realise that the driving force behind the proposition of exotic dark matter solutions is not the non-existence of normal matter solutions, but rather the inability of these solutions to completely address the missing matter.  Because this report is focusing on non-baryonic solutions, this section will not go into great depth.  However, objections to each baryonic object as a solution will be identified.

Red Dwarfs and Brown Dwarfs

A star’s brightness (and hence detectability) depends upon its mass.  Bigger stars are rarer than smaller stars, and there are many of these small stars in the galaxy.  Red Dwarfs have 0.5 to 0.1 solar masses, and are incredibly common.  If these stars are more numerous than sun sized stars then could they account for the missing mass?  Unfortunately, the smaller mass offsets the greater quantity, and whilst making a contribution to the mass not detected, this contribution is rather small.  To achieve the mass required, the numbers would need to be greater, which would require more visible stars to maintain predicted ratios[xiii]. When a collapsing mass of primordial gas does not have sufficient mass to achieve nuclear fusion via gravitational collapse, the resulting object is called a brown dwarf, and emits EMR via gravitational collapse.  These object may be 16 times the size of Jupiter to .05 times the size of the sun.  Similar objections to those for red dwarfs exists against these objects contributing significant mass to galaxies.

Planets, rocks and dust

Whilst planets are indeed difficult to detect, a number of factors rule them out.  Firstly, using the solar system as an example, 99% of the mass of the solar system is in the sun.  There is no reason to suggest this is not the case for other star systems, and therefore there contributions are negligible.  Secondly, unlike stars and dwarfs, planets are made up of heavy elements that are produced in stars.  Such elements make up only 1 % of all matter.

Hydrogen gas

Whilst abundant, hydrogen gas is readily measurable via its radio spectrum, and the quantities detected do not significantly address the dark matter problem.  Later discussions on limits to baryonic matter also impact the role of hydrogen gas.

Stellar Remnants

When stars reach the end of their lifecycle, they may take on a number of forms.  Which form they take is related almost entirely to mass.  Objects with less the 8 solar masses will shed a large volume of their mass, and collapse into a small object with a very large density - white dwarfs, which emit radiation caused by their gravitational collapse.  When they eventually cool, they become black dwarfs.  Because they contain only a small amount of a stars mass (the rest being lost to solar winds or supernova explosion) , they do not represent a significant mass contribution to the galaxy.  Further, the smaller a star, the longer its lifespan.  Therefore, relatively few stars in the galaxy under 8 solar masses would have reached this stage of their evolutions. For stars with greater masses, the remaining mass overcomes the force holding atoms together (keeping protons and electrons apart), and these stars collapse to a super dense object called a neutron star.  These object contain large amounts of mass in a small volume, and could thus contain a large proportion of mass in a hard to detect form.  However, just as smaller stars are more common, larger stars are rarer, and this rate falls off exponentially.  Therefore, stars capable of forming neutron stars are much rarer, and would fail to provide any significant mass. Even larger stars may become black holes, objects so dense that their escape velocity exceeds the speed of light.  This makes them very hard to detect (very dark matter), but as they are even rarer than neutron stars, the same arguments apply.

Big Bang Nucleosynthesis and limits to baryonic mass

Beyond these arguments, which focus on matter at a galactic level, there are more fundamental limitations to the amount of baryonic matter that exists in the Universe.  The most accepted explanation for the formation of the universe is the Big Bang theory, whereby the universe was created from a large explosion (to put it mildly), that created time, space and matter.  Whilst the details have not achieved consensus, there are a number of agreed facts that affect dark matter.  In the first moments, the universe was incredibly dense and incredibly hot (10³⁸ K).  Particles were not differentiated, but as the universe expanded and cooled, particles began to form from the baryonic matter (protons and neutrons) in the universe.  Deuterium (²H or D), Helium 3 (³He) and Helium 4 (⁴He), as well as small quantities of Lithium  (⁷Li) and Tritium (³H), were formed as nucleons merged into atomic nuclei.  The majority of protons did not mix, and became Hydrogen nuclei[xiv].  This process is termed Big Bang Nucleosynthesis (BBN). Particle physicists have developed models to show the relative proportions of the elements created under varying levels of baryonic density, which is shown graphically in figure 2.  Observations of current abundancies of these elements are shown by the white boxes.  The key observations is Deuterium, which can only be destroyed by astronomical processes not created.  Studies by Burles and Tytler in 1997 have made a strong case for a current D/H ratio of (3.4±0.3)×10^-5 [xv].  Studies of ⁷L abundance support this range.  Such a range gives an initial baryonic density of (3.8±0.4)×10^-31g cm ^-3, as shown by the orange bar.

Figure 2 – Big Bang Nucleosynthesis particle quantities [xvi]

Knowing the baryonic density and the size of the universe allows us to determine the upper limit of the mass of baryonic matter created during BBN.  Current estimates place Ω^B at 0.05.  Using the estimate of Ω^M at 0.4, baryonic matter represents roughly 10% of the mass of the universe.  This in turn places an upper limit on the potential contribution of baryonic objects to the missing mass, and drives the need for non-baryonic alternatives.  Figure 3 gives a summary of a leading model of the mass constituents of the universe.

Figure 3 - Mass components of the universe[xvii]

Inflationary Theory

The logic of the above arguments centers around Ω=1.  At first glance, it would appear that there is no reason for the universe to be flat – its density may well be much lower than Ω=1, and therefore expand indefinitely.  However, there were a number of problems with the initial big bang model totally unrelated to the dark matter problem.  In summary, the key issues were:

• lack of antimatter – BBN predicts the creation of anti-particles in equal numbers, yet anti-particles are rarely observed
• galaxy formation in an expanding universe – what causes the compact homogenous early universe to clump into structures that would develop into galaxies?
• mass density close to unity – whilst the value of Ω is debated, it is very close to one, which seems awfully coincidental given that it could well have been
• uniformity – cosmic background radiation (CBR) studies[xviii] shows the distribution of photons to be remarkably uniform across the universe
• horizon vs. uniformity – the speed of light limits the distance over which two areas can ‘communicate’, and yet the universe is uniform over distances far greater than this limit

Inflation addresses all of these problems, and is currently viewed as the most likely description of the primordial universe[xix].  It predicts that at an early stage in the universe (about 10^-35 seconds), the universe underwent a very brief (10^-32 seconds), rapid expansion, increasing in size by roughly 10^50[xx].  This process was driven by vacuum energy, which can be seen as circumstances causing gravity to exert a massive repulsive force[xxi].  Whilst counter-intuitive, the process is consistent with our current understanding of physics.  The key impact of inflation on the dark matter problem is its prediction that Ω=1.  The reasoning behind this is that inflation produced such a massive universe, that the observable universe is an insignificant portion (10^-24 – 10^-1000), “astronomers are observing such a tiny part of our domain the they must conclude that space has zero curvature”[xxii].  This implies that there exists a sea of particles to achieve unity.

Non-baryonic candidates for dark matter

Given the overwhelming evidence for a large quantity of non-baryonic dark matter, we will now discuss potential candidates for the exotic dark matter.  The forces that cause matter to interact have several important implications for dark matter, so a brief introduction is required. There are four known forces in the universe: electromagnetic force, which holds atoms together, and drives chemical reactions; strong nuclear force, which holds protons together in the nucleus of an atom, where electromagnetic repulsion would push the positive particles apart; weak force, which drives particle decay reactions; and gravitational force, which has been discussed previously. Despite there being four separate forces, many physicists believe that these are manifestations of a single force, and that at early in the universe (perhaps 10^-40 seconds) these forces were one.  Such theories are termed Grand United Theories (GUT) or Theories Of Everything (TOE).  GUT tend to focus on weak, strong and electromagnetic, whilst TOE includes gravitational force.  GUT predicts a number of stable particles that offer potential candidate for dark matter. Dark matter can be defined as hot or cold dark matter (HDM and CDM).  This relates to the energy levels and velocities of the particles, which have important implications for their distribution and gravitational interaction.  HDM is defined as matter that had relativistic speeds when created, and although having slowed over time, is still moving at a far greater velocity than CDM, which has reached thermal equilibrium.  Current theories predict a mixture of HDM and CDM.

Massive Neutrinos

The existence of neutrinos has been predicted since the 1930’s[xxiii], and were originally believed  to be massless (and possibly undetectable).  However, a number of experiments since the 1960’s have detected neutrinos (mostly emitted from the sun), and recent experiments have confirmed they do indeed possess mass (Sunbury Neutrino Observatory[xxiv], Super-Kamiokande[xxv] and detections from the Supernova SN1987A) - hence the term massive neutrinos, which whilst implying they are particularly heavy, merely acknowledges they possess mass. Neutrino production is predicted by BBN, although they cease to play a role in particle evolution after about 1 second[xxvi].  The standard model predicts a neutrino density of 337 cm^-3[xxvii].  It is believed that neutrinos have three types (termed flavours), matching the three classes of leptons – electrons, muon and tauons.  The number of neutrino flavours has important implications for BBN, and the existence of more or less flavours would impact the Hydrogen/Helium ratio in the universe[xxviii], which would contradict observations. The mass of the neutrino is the key to determining its contribution to dark matter, but because they only interact with matter using the weak force, and such interactions are very rare, no exact mass has been deduced, although upper and lower bounds have been determined, .054 eV being the current lower limit[xxix].  The upper limit is determined by structure in the universe, with 2.2 eV (Mainz) being the most recently cited value[xxx].  The upper values for muon neutrinos and tau neutrinos are 170 KeV and 15.5 MeV respectively[xxxi].  Because of the variation of values for neutrino mass, it is difficult to gauge their overall impact on the mass of the universe, and its contribution to the missing matter problem.  However, the properties of neutrinos provide indications of it likely role. Neutrinos are an example of hot dark matter.  Their high velocity has a number of consequences.  Firstly, the higher velocity requires a greater mass for clumping to occur.  This means that HDM will form into large clumps, the size of super clusters, but not galaxy sized ones.  This implies that the universe started as super cluster sized objects, that broke down into clusters, and the into galaxies. There are two key objections to galaxies being created from super cluster sized objects (termed the Pancake model).  Firstly, insufficient time has elapsed since the formation of the universe for galaxies to have formed[xxxii].  Secondly, computer simulations of galaxy formation using HDM failed[xxxiii].  In addition to these objections, HDM’s large scale makes it non-applicable for smaller scale dark matter problems.  Of particular difficulty are dwarf galaxies, where the density of neutrinos required to maintain structure would exceed to the Pauli exclusion principle – the density of neutrinos required would be greater than the laws of quantum physics allow[xxxiv]. Finally, work by Turner, shown in Figure 4, plotted power spectrum at varying mass densities, along with forecasts for various dark matter candidates.  At higher frequencies, a 100% contribution of HDM to dark matter do not correlate with observed data, indicated the HDM cannot provide a total solution to the dark matter problem.

Figure 4 - Power Spectrum of Mass Density[xxxv]

Cold Dark Matter

Whilst HDM has a number of downfalls, its chief advantage is that the proposed particles have been observed,  CDM, by comparison, requires the existence of particles that not only have not been detected, but may well be undetectable.  A number CDM candidate particles have been proposed.

Supersymmetry particles

Supersymmetry theory proposes a mechanisms for unifying all four physical forces, and involves uniting two categories of particles – fermions and bosons. Fermions are the building blacks of matter, whilst bosons provide the mechanisms that cause fermions to be pushed apart are stuck together.  For each fermion there is a matching boson[xxxvi]:

Fermion          Boson

electron           selectron photino            photon gravitino          graviton Electrons, photons and gravitons are familiar to us, but there companion particles are not.  Many companion particles predicted by supersymmetry have brief half-lives, however, a particle called the lowest supersymmertic particle (LSP) is predicted to be stable, having no lesser forms to decay into.  In supersymmetry, various theories favour the photino[xxxvii], gravitino[xxxviii] and neutralino[xxxix] as the LSP, and therefore a potential dark matter candidate.

Cosmic Strings

Cosmic String theory is another GUT, which predicts the existence of ‘strings’, created during ‘phase transitions’ (shifts in the properties of the universe, such as the dislocation of forces) in the early universe.  These strings would be very thin (less than the width of a proton) and very dense (a 1.6 km string would have the same mass as the earth)[xl].  Strings may evolve through breakages caused by vibrations than would allow strings of many sizes to exist in the current universe.  If these strings survived into the present universe, they would help explain some structural features of the universe (e.g. filaments in super clusters[xli]), and their gravity could act as a catalyst for galaxy formation. As with all CDM, the key objection to cosmic strings is the lack of evidence for their existence.  Also, string theory predicts oscillations in the strings at near light speed, which gives off gravitational waves, causing the strings to dissipate, meaning they may not exist in the present universe[xlii].

Axions

Another prediction of another GUT – the Peccei-Quinn symmetry model – axions exist to explain the lack of charge and parity violation in strong force interactions, created during phase transitions or string decay[xliii].  Whilst low masses are predicted – 10^-3 eV – quantities sufficient to contribute to missing mass are predicted, and axions cluster effectively to form galaxies and large-scale structure[xliv].  Once again lack of evidence for their existence is the key barrier to this theory, although predictions of annihilation into a single photon in a strong magnetic field have driven a number of experiments[xlv], with no success to date. Whilst this is not a complete inventory of CDM candidates, it covers those particles with the strongest evidence.  Combining the HDM and CDM candidates, we can speculate at the likely contribution of these particles to the dark matter problem.

Implications of non-baryonic matter solutions

As show by Turner, HDM cannot provide a complete solution to the dark matter problem.  However, there is strong evidence for the existence of neutrinos, with a predicted cosmic neutrino background of 1.9K[xlvi], indicating that HDM is likely to play some part in the picture.  This leads to a mixture of HDM and CDM, sometimes called the mixed dark matter (MDM) solution.  The key benefits of the MDM solution is that the strengths of the two theories can be combined, and the weaknesses offset by properties of the other. With regards to large scale structure (super clusters, filaments, bubbles and voids), HDM offers a good candidate for providing the gravitational frame work, whilst CDM allows the formation of galaxy sized structures in acceptable time frames.  Likewise, CDM offers potential solution s to dwarf galaxy dark matter problems, and most galactic dark matter phenomenon, where HDM is shown to be an unworkable solution.  CDM./HDM ratios of 70/30[xlvii] are cited by astronomers. Mixed dark matter solutions also offer some additional benefits[xlviii]:

• the power spectrum shape is a better fit to observations, as shown in figure 4.
• observations indicate the need for a more weakly clustering component of dark matter
• HDM may offset an over-dense central dark matter density in pure CDM dark matter halos

Finally, a number of computer simulations using MDM have achieved results that correlate with observations of galactic and cosmic structure, including Faber, Blumenthal & Primack, Melott & Centrella and Davis & White[xlix]. How much progress will be made in the near future is uncertain.  Although some particles (such as axions) may be detectable through experimentation on predicted properties, most of the CDM candidates exist from a time when the temperature of the universe was much higher than those that can be replicated at present or in the near future.  Whilst particle accelerators have offered great insights into the nature of matter, no CDM candidates have yet been produced using this technique. Like black holes, whose direct evidence is impossible from earth, astronomers will seek to gather as much evidence to support or disprove various dark matter candidates, and may potentially provide such an overwhelming case (as has been achieved with black holes), to anoint a prime candidate for the dark matter solution.  Or as is the case in many large problems, several complimentary solutions may emerge.

[i] Parker, B. “Invisible matter and the fate of the universe”, Plenum Press, 1989, p.215 [ii] http://www.ess.sunysb.edu/fwalter/AST248/week2.html [iii] For most objects in the universe, this law is sufficient to study the gravitational interaction between them.  Einstein’s theory of relativity expand Newton’s theories, dealing with very massive objects and objects moving at speeds approaching the speed of light. [iv] http://www.astro.ucla.edu/~agm/darkmtr.html citing Bartusiak, Marcia. “Through a Universe Darkly”. New York: Harper-Collins, 1993. [v]  http://www.astro.ucla.edu/~agm/darkmtr.html [vi] http://www.astro.ucla.edu/~agm/darkmtr.html [vii] although stars with eccentric orbits do exist [viii] http://wannier.jpl.nasa.gov/recent_research/extragalpaper/ [ix] http://nedwww.ipac.caltech.edu/level5/Ferguson/Ferguson3_3.html [x] http://www.astro.ucla.edu/~agm/darkmtr.html [xi] Although recent x-ray evidence indicates a much greater quantity of galaxies than originally identified - http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/990924a.html [xii] Turner, M. “Dark Matter and Dark Energy in the Universe”, The Third Stromlo Symposium: The Galactic Halo, 1999 [xiii] Parker, et al [xiv] It was much latter in the universe’s evolution that conditions allowed electrons and atomic nuclei to form whole atoms – 700,000 years – source http://csep10.phys.utk.edu/astr162/lect/cosmology/hotbb.html [xv] http://nedwww.ipac.caltech.edu/level5/Primack/Primack1_4_5.html [xvi] Turner, M. et al [xvii] Turner, M. et al [xviii] Overwhelmingly supported by the COBE satellite study - http://space.gsfc.nasa.gov/astro/cobe/cobe_home.html [xix] http://nedwww.ipac.caltech.edu/level5/Guth/Guth4.html [xx] http://csep10.phys.utk.edu/astr162/lect/cosmology/inflation.html.  These figures are current estimates.  Parker, et al. refers to 10^-36, 10^-30 and 10²⁸ for starting time, duration and expansion factor. [xxi] See http://nedwww.ipac.caltech.edu/level5/Guth/Guth_contents.html for a more detailed discussion of inflation [xxii] Tucker, W. and Tucker, K. “The Dark Matter”  p.127 [xxiii] initially by Wolfgang Pauli [xxiv] http://www.sno.phy.queensu.ca/ [xxv] http://www.ps.uci.edu/~superk/sk-info.html [xxvi] http://csep10.phys.utk.edu/astr162/lect/cosmology/hotbb.html [xxvii] http://www.astro.ucla.edu/~wright/neutrinos.html [xxviii] http://www.astro.ucla.edu/~agm/darkmtr.html [xxix] http://www.oxy.edu/~kirkpatj/darkmatter.main.deeper3.htm [xxx] http://cupp.oulu.fi/neutrino/nd-mass.html [xxxi] http://cupp.oulu.fi/neutrino/nd-mass.html [xxxii] Parker et al, p.158 [xxxiii] Parker et al, p.160 [xxxiv] Parker et al, p.161 [xxxv] Turner, M. et al [xxxvi] Protons and neutrons are made of smaller particles called quarks, and are not dealt with directly in this model [xxxvii] http://astron.berkeley.edu/~mwhite/darkmatter/essay.html [xxxviii] http://nedwww.ipac.caltech.edu/level5/Primack/Primack1_5_1.html [xxxix] http://web.mit.edu/~redingtn/www/netadv/specr/6/node3.html [xl] Tucker et al, p.193 [xli] http://www.pbs.org/wgbh/aso/databank/entries/dp76st.html [xlii] http://www.pbs.org/wgbh/aso/databank/entries/dp76st.html [xliii] http://www.astro.princeton.edu/~dns/MAP/Bahcall/node16.html [xliv] http://www.astro.princeton.edu/~dns/MAP/Bahcall/node16.html [xlv] http://web.mit.edu/~redingtn/www/netadv/specr/6/node1.html [xlvi] http://antares.in2p3.fr/Overview/why.html [xlvii] http://www.vuw.ac.nz/~mackie/royal_society/nzst_article/universe.htm, http://hermes.physics.ox.ac.uk/users/Galactic/layman/dark.html [xlviii] http://nedwww.ipac.caltech.edu/level5/Primack/Primack1_7_6.html [xlix] Parker et al, p.182