Chapter 5: The Complicated Universe:

Dark Matter, Structure Formation, Inflation and Hidden Galaxies


In this final chapter we consider some of the more puzzling aspects of cosmology that have emerged in the last 15 years. New observations have raised considerable challenges to our understanding to the point where we realize that the Universe is far from simple. Here we will consider four relatively new ideas:

  • Dark Matter: This topic illustrates our profound ignorance of the Universe. We will detail the evidence that suggests the Universe consists mostly of an unknown form of matter that doesn't emit light. The majority of this chapter will be concerned with this topic. Its probable existence means that we really are missing a fundamental piece of knowledge about the Universe as we don't know the form of most of its mass.

  • Structure Formation: We will briefly review the large scale clustering of galaxies in the Universe. This is directly related to the distribution of dark matter and unraveling the patterns is very challenging. These patterns were introduced in Chapter 4 via Figure 4.8.

  • Inflation: This is an important new component of our basic Hot Big Bang model that is necessary to solve some paradoxes of the standard Big Bang model. Inflation makes a definite prediction about the geometry of the Universe and an indirect prediction about how much dark matter must exist. As we will see, inflation demands a spatially flat Universe. This is most easily achieved if W = 1. This is why we kept considering W = 1 models in the previous discussion because they are theoretically attractive in the context of the inflationary model. However, spatial flatness is really a combination of W and L so that inflation really demands W + L = 1.0. In its simplest form, this is achieved with W = 1 and L = 0. However, there is little evidence that W = 1 and hence, if one accepts inflation then one is driven to a positive value for L.

  • Hidden Galaxies: We conclude this chapter with a brief discussion about a new population of galaxies that has been discovered in the last 10 years. These galaxies, known as Low Surface Brightness galaxies may actually dominate the galaxy distribution but their presence has been hitherto unknown due to the difficulty of detecting them.

    Dark Matter

    Objects which emit light, whether they are cigars, light bulbs, cows, stars or galaxies can be characterized by their emitted energy per unit mass. This is parameterized as the Mass to Luminosity ratio or M/L. For cosmological purposes, it is most convenient to express M/L in terms of solar masses and luminosities. For main sequence stars it can be shown that L is proportional to M3.5-4 . Thus, a 10 solar mass star star has M/L of approximately 0.001, a 1 solar mass star has M/L =1 and a 0.1 solar mass star has M/L of approximately 1000. The term "dark matter" refers to the the existence of objects which have extreme M/L. Identifying the nature and extent of the dark matter component in the Universe is, arguably, the most significant unsolved problem in all of cosmology.

    The amount of dark matter directly impacts our measurements of W. The mass density of the Universe is insensitive to the actual nature of the mass. The only requirement is that this mass gravitates. This requirement can be met if the dark matter is composed of a small space density of very massive objects or a large space density of very low mass objects. It is the total integration of this mass-density over spacetime that determines W and the overall large scale geometry of the Universe. The dark matter may reside in galaxies or it may be distributed between the galaxies.

    In principle, the dark matter content of the Universe could be extreme. While we don't know the exact form, distribution or amount of dark matter we do know the following: if the Universe is closed it is fairly simple to calculate the amount of mass density that must be present to close it. This depends on the critical density which was derived in Chapter 4 and that depends only on Ho. Since Ho is known to within a least a factor of 2, then the critical mass density is known to within a factor of 4. If we compare the required mass density to close the Universe, the closure density, to the total amount of stars and galaxies that are visible as a result of their emitted light we reach an astounding result:

    If the Universe is closed then no more than 1% of its total mass is in the form of luminous stars and galaxies.

    One percent! That means that, in principle, 99% of the Universe is composed of dark matter. Ninety-nine percent! That means we know next to nothing about the fundamental nature of the Universe. This is embarrassing but is it this correct? How do we know dark matter is really out there?

    Evidence for Dark Matter

    Local Scales

    In general, the evidence for dark matter is a result of analyzing the motions of test particles on some scale and seeing if there is enough mass that can be accounted for by the light emitting objects on that scale to produce the observed motion. If there is not enough light, then some other form of matter must be providing the mass. An example of this process in which we can be sure there is no dark matter, is the case of our Solar System.

    The first historical success of using perturbed motions to find matter was the discovery of Neptune in 1846 from the observed perturbations in the motion of Uranus. In the 20th century, a similar analysis of Neptune allowed for the discovery of Pluto in 1930. These successes spurred on efforts to discover a planet beyond Pluto, known as Planet 10 as the combined masses of Neptune and Pluto weren't quite enough to account for the observed perturbations in the orbits of the outer planets. Interestingly, the close passage of Voyager II near Neptune in 1989 allowed for a significant refinement of the mass of Neptune. This proper accounting of Neptune's mass removed the need for the existence of Planet X and indeed there is no longer any evidence for unaccounted mass in the Solar System. So, on the scale of the Solar System, there is no dark matter. All the mass that is needed to drive the orbital evolution of the Solar System is fully accounted for.

    Similarly, if one analyzes the motions of nearby stars around us to constrain the local mass density of our place in the disk of our Galaxy, there is no strong evidence for dark matter. But, a census of the mass in our neighborhood is interesting. The total mass density that has been inferred is approximately 0.18 solar masses per cubic parsec. Testing for the presence of dark matter in the solar neighborhood now becomes an accounting problem. The possible sources of this mass in the solar neighborhood are 1) luminous stars, 2) interstellar gas, 3) stellar remnants (mostly white dwarfs) and 4) dark matter. Observations indicate that approximately 0.1 solar masses per cubic parsec of mass density is in the form of luminous stars (including the thick disk component of our Galaxy). This implies additional mass not in the form of luminous stars but it can readily be accounted for. Approximately 0.05 solar masses per cubic parsec is in the form of gas (gas gets turned into stars, of course), and the remaining 0.03 solar masses per cubic parsec is in the form of white dwarfs (stellar evolutionary end points of low mass stars).

    The reason we discuss this here is to emphasize that simple stellar evolution ultimately produces objects with high M/L values. In a few billion years when star formation has ceased in our Galaxy, most of the stars will fade into their stellar remnants (black holes - a good form of dark matter(!), neutron stars or white dwarfs). In this sense galaxies are destined to end up "dark". It is interesting to speculate that some galaxies may have achieved this state already. Indeed, a possible detection of this population is discussed at the end of this chapter.

    Galaxy Halos

    Figure 5.1 The spiral galaxy NGC 253 seen edge on.

    On scales of galaxies and clusters of galaxies, there is ample evidence for dark matter. This comes from the form of galaxy rotation curves. Figure 5.1 shows an image of a typical edge-on spiral galaxy, where the thin disk and central spherical light concentration are evident.

    Figure 5.2 Schematic representation of the rotation curve of a galaxy. If most the mass of the galaxy is in the center, then one expects smaller rotational velocities with increasing distances from the center of the galaxy. This is shown in the dashed line and is not what is actually observed. Instead, rotation curves of the form depicted by the solid line are observed. The observation that the rotational velocity is constant after some radius implies that the mass of the galaxy must be in a greatly extended (relative to the light) distribution.

    If the distribution of light traces the distribution of mass, then we would expect a high mass concentration that corresponds with the bulge light. In that case, the galaxy is similar to the point mass approximation that governs Solar System orbits in which the orbital velocity decreases with distance from the point mass. The expected rotation curve would then look like the dashed line shown in Figure 5.2. Observations, however, reveal a significantly different picture as most all galaxy rotation curves have a rotational velocity that rises slowly and then flattens out. This is shown as the solid line in Figure 5.2.

    Figure 5.3 A rotation curve of a spiral galaxy. The center of the galaxy is at r = 0 and both halves of the galaxy rotation curve are shown here. The higher velocity side is rotating away from the observer and the lower velocity side would be rotating towards the observer. The galaxy quickly reaches its maximum rotational velocity at a relatively small radius and maintains that velocity out to the limits of the data.

    In Figure 5.3 we show a typical rotation curve for a real spiral galaxy. These data show that the point mass approximation is invalid. The existence of flat rotation curves of galaxies can only be explained if the mass of the galaxy is increasing in direct proportion to the radius. We can understand this by referring to the derivation of Kepler's Third Law that was done in Chapter 1. Newton was able to show that for an object in circular orbit, the orbital velocity is determined by the total mass enclosed within the radius. In equation form, this is given by

    M(r) ~ V2 R

    Flat rotation curves mean that V and hence V2 is constant. The only way that can be achieved is if M(r)/R is a constant. Thus, the enclosed mass M(r) must continue to increase with increasing radius. However, since the light intensity is decreasing with increasing radius, this means that there must be substantial amounts of dark matter located at large radii in galaxies or, more specifically, that M/L must increase with increasing R.

    Flat rotation curves can be reproduced in a model that assumes that most of the mass of the galaxy is distributed in a spherical halo around the disk. Since these halos contain very little light, they must be composed mostly of dark matter. Analysis of galaxy rotation curves suggests that approximately 90% of the mass of the galaxy is in the form of dark matter which is distributed in a spherical halo around the galaxy.

    But why can't galaxy halos just be composed of stellar remnants? For instance, a galaxy halo that was composed of black holes would certainly be dark yet provide enough mass to account for the observed flat rotation curves. This can be ruled out by a very simple but powerful argument. A black hole is the endpoint evolution of a massive main sequence star. Thus, the object that is now the black hole wasn't always black. There was a period when it was producing light. Hence, if galaxy halos are now composed of black holes or other remnants, there would have been a time in the past when the halo was full of luminous stars. As we look out farther in distance we are looking back in time due to the finite speed of light. Hence, halos should be bright when galaxies are younger but observations of distant galaxies do not show any evidence for luminous halos as a function of look-back time. As a result we can rule out galactic halos as being composed of mostly stellar remnants.


    There is another interesting possibility for the constituents of the halo that has recently been tested via a novel known as gravitational microlensing. In brief, when light passes very close to a star, General Relativity tells us that it must bend because it is traveling through curved space and photons are effected by gravity as they have an energy related mass. Einstein's theory predicts the existence of objects known as gravitational lenses. A gravitational lens acts just like a normal lens in that it can bend (refract) light as well as amplify the brightness of a distant light source. The unique character of gravitational lensing is that it's achromatic. There is no equivalent to the index of refraction for a normal lens as the behavior of light passing through curved spacetime is independent of its wavelength. Thus, a gravitational lens will effect both the blue and red portions of the spectrum equally and this is its unique signature.

    If a significant fraction of the dark matter in the halo of our galaxy is composed of objects like brown dwarfs or planets then there will be occasional amplification of the light from extragalactic stars by the microlensing effect just described. These microlensing events, however, would be extremely rare. Thus, to detect them would require imaging a few million extragalactic stars a night to search for the one or two that might vary in brightness over the course of a year due to microlensing. Now of course, in any field of a million stars, many of the objects would be naturally variable. However, intrinsic stellar variability (novae, binary stars, pulsating stars) always shows wavelength dependent behavior. That is, the variation in the blue would be different than the variation in the red.

    In a spectacularly heroic experiment known as the MACHO project (MACHO stands for MAssive Compact Halo Objects), astronomers have monitored the brightnesses of millions of extragalactic stars in the LMC (the LMC is located directly behind our Galactic Halo) for the past 4 years and have now detected about a dozen events that can be reliably associated with microlensing. A signature of a lens event is shown in Figure 5.4 where it can be seen that the variation of the star in the blue and the red is identical. That means its light was amplified by microlensing. The duration over which the amplification event occurs (the event in Figure 5.4 lasted about 20 days) is related to the mass of the lens. The major result that the MACHO survey has produced to date is the total absence of short duration events which would be caused by lensing objects of a few Jupiter masses. This means that the halo of our Galaxy cannot be filled with sub-stellar mass objects. The bulk of the lensing events in the halo detected to date can be explained by regular stars (possibly some white dwarfs), of mass about 0.5 M solar masses.

    Figure 5.4: Signature of a gravitational lens amplification of starlight. The degree of amplification and the shape of the light curve is identical in the red and blue filters. This is the unique signature of a gravitational lens. The duration of this lens event was approximately 20 days

    Clusters of Galaxies

    Figure 5.5 A typical cluster of galaxies. The individual members do not escape from the cluster as sufficient mass exists to prevent the expansion of the cluster.

    Clusters of galaxies represent a region of the Universe in which the mass density is sufficiently high that the expansion has been overcome. An example cluster is shown in Figure 5.5. This mass density serves to randomize the velocities of the cluster members as they assume some orbit in the cluster of galaxies. In that sense, galaxies in clusters are very much like the molecules inside a balloon of fixed volume. The galaxies can't escape and their overall relative velocities are determined by the mass of the cluster. The molecules in the balloon can't escape either and their overall velocity is determined by the temperature of the balloon. Thus, in a cluster of galaxies mass is analogous to temperature and indeed, this analogy explains why clusters of galaxies often emit X-rays. If the cluster is sufficiently massive it can heat the intracluster gas to high temperatures where it emits X-rays. This gives us an immediate diagnostic tool.

    If we simply measure the relative velocities of the galaxies we can infer the total mass of the cluster. A small complication enters in that one needs to know the exact shape of the cluster; a spherical cluster is different than one that is shaped like a pancake - but the general principal applies. That dynamical mass estimate can then be compared to the mass estimate based on counting the number of galaxies in the cluster and adding up all their light. When this is done, it is typically found that the luminous galaxies in the clusters can only provide 5-10% of the total mass required for the cluster to exist. Taking into account the mass provided by the hot intracluster gas only raises this contribution by about a factor of 2.

    Figure 5.6 The cluster Abell 2218. The appearance of "arcs" in the image is a manifestation of the distortion of the images of background galaxies by the lensing mass of the cluster.

    Another means of estimating the mass of a cluster again appeals to gravitational lensing. In this case, it is the entire mass of a cluster that acts collectively as a lens. Figure 5.6 shows a spectacular example of this phenomena. Here, numerous arc-lets and rings can be seen. These are the distorted (lensed) images of resolved galaxies located behind the cluster. The orientation and degree of curvature of these features depends upon the cluster mass distribution and the overall amount of mass. Again, when the mass is inferred in this manner and compared to the luminous galaxies in the cluster, a substantial mass discrepancy exists. When this evidence is combined with the velocity data, there is little doubt that in clusters of galaxies, a substantial amount of dark matter must be present.

    Intergalactic Dark Matter

    An open question currently, yet a very important one, is whether or not there exists a substantial population of dark matter that is located in Intergalactic space - that is the space between galaxies and/or clusters of galaxies. If there is none, then dark matter is strictly confined to galaxies and clusters of galaxies. In that case we would expect W to be in the range 0.1 - 0.2 which is consistent with the determinations of W discussed in Chapter 4. However, when we discuss Inflation later on in this chapter we will see that it strongly prefers W = 1.0. Our dark matter census is well short of this value. Therefore, studies of the dark matter in galaxies and in clusters of galaxies has produced two important results: a) there is dark matter located there and b) there is not enough dark matter located there to close the Universe. Thus, if the Universe is closed (W > 1.0), then substantial amounts of dark matter has to exist in Intergalactic space where there are no galaxies. Thus, it is possible that there are two kinds of dark matter, that which is present in galaxies or in clusters of galaxies and that which is present outside of these regions.

    Possible Kinds of Dark Matter

    In considering the kinds of dark matter there are two broad possibilities. Normal dark matter is composed of baryons and is referred to as baryonic dark matter. An important feature concerning baryonic dark matter is that it wasn't necessarily always dark. A stellar mass black hole is the prime example as it once was a star radiating energy. Exotic dark matter would be non-baryonic in nature and is most probably in the form of some strange particle, hitherto undetected. In addition to important physical differences there may be an important philosophical difference. Astronomers want to build big telescopes in order to probe over vast distances and solve cosmological problems. But astronomers can only detect and measure baryons. If the mass of the Universe is mostly non-baryonic, then its fundamental nature will not be revealed through telescopic observation, but rather in some high energy accelerator experiment on the Earth. It is thus highly regrettable that continued funding of the Superconducting Super Collider was denied, as this might have been the grandest cosmological experiment ever done.

    Some candidate forms of dark matter are listed below:

  • Bricks: A brick is an excellent candidate for dark matter as it has very high M/L. Closing the Universe with bricks, however, is not possible because bricks are made of heavy elements and would have therefore required a lot of massive stars to exist previously to make these heavy elements. This is not observed so the Universe is not filled with bricks.

  • Small Balls of Hydrogen. A Jupiter mass ball of hydrogen would have high M/L in the optical bands. The mass of Jupiter is approximately 0.001 solar masses and the required space density to have our mass dominated by these objects would be around 10 Jupiters per cubic parsec. This space density only contributes 0.01 solar masses per cubic parsec of mass density in the solar neighborhood. Hence, the survey of the distribution of mass in the solar neighborhood discussed previously would be unable to rule out the presence of this population. On the other hand, the gravitational microlensing experiment described earlier places very strong limits on the space density of this population. These limits are so strong that very little of the total mass of the galaxy can be in this form.

  • Stellar remnants: Since the Galactic disk is not yet old enough for white dwarfs to cool down to temperatures below a few hundred degrees K (and hence become invisible) or neutron stars to slow down and cease being pulsars (and hence become undetectable), the only viable high M/L remnant that would escape local detection is stellar mass black holes. As discussed before, while black holes are an excellent example of dark matter, they used to be bright, massive stars and hence would have been visible in the past. Moreover, since massive stars produce the bulk of the heavy elements in the galaxy, then they leave behind a chemical tracer of their existence. If the dark matter in our Galaxy is dominated by a population of black hole remnants, then its heavy element content should be much larger than is actually observed. This in fact raises the general expectation that the production of baryonic dark matter (in the form of stellar remnants) is directly related to the chemical evolution of a galaxy. Galaxies with more heavy elements in them should have more stellar remnants and more baryonic dark matter. While there is some observational support for this, the amount of heavy elements that would have been produced by a pre-existing population that has now produced black hole remnants would be sufficient to start an Interstellar gold rush. Hence, the mass of our galaxy can't be dominated by black hole remnants either.

  • Big Stellar Remnants: Globular Clusters are the oldest known stars in our galaxy and may have been the first objects to form in the Universe. However, Globular Clusters do show signs of chemical enrichment. To account for this, theorists have postulated the presence of a population of very massive stars (10,000 solar masses and higher) that formed prior to the formation of globular clusters and seeded the Universe with a few heavy elements. These very massive objects (VMOs) could have coalesced together into a very large stellar remnant, say a one million solar mass black hole. There would only have to be a million of these objects in our galaxy for the total mass to be dominated by them. However, if this were the case we would expect one of these objects to orbit through the galactic plane every 100 years and swallow up lots of gas and dust and have a very visible manifestation. Hence, VMO remnants are not a likely candidate either.

  • Quantum Black Holes: An intersection between General Relativity and the precepts of quantum mechanics allows for the existence of a very unusual particle - a mini black hole. A mini black hole has a mass equivalent to that of a large terrestrial mountain, about 1015 grams and a radius of 10-13 cm. Such an object could only be created by tremendous compressional forces which might have been present in the very early Universe. As the radius of a mini black hole is like that of a nucleon, it is a quantum mechanical system and energy can leak out. As energy leaks out, mass is lost and the system shrinks which accelerates the energy loss. Mini black holes are then destined to "evaporate". The last stage of this evaporative process is the sudden release of high energy photons (gamma rays). For a mass of 1015 grams the evaporation time scale is 10 billion years. Amazingly enough, a population of gamma ray bursters has been detected in the last 3 years. However, no one believes this population is due to evaporating mini black holes.

    Non-baryonic Dark Matter

    By any measure, if W = 1 then the Universe is dominated by non-baryonic dark matter. This form of dark matter would be a particle, like a neutrino or a WIMP (discussed earlier). Furthermore, that dark matter must be distributed more smoothly than the light and be distributed between the galaxies as well as in galaxies. In this scenario, the Universe is a sea of non-baryonic dark matter with little bits of baryonic material (e.g. galaxies) floating about in it (in spirit, similar to the cosmology of Thales in Chapter 1).

    Non-baryonic dark matter comes in two basic forms: hot and cold. Hot dark matter (HDM) means the particle is relatively light so that when it was initially created in the early Universe it moved near the speed of light. There is only one strong candidate for HDM and that is a neutrino. In the late spring of 1998, new experimental data on the mass of the neutrino was released. That data is very discouraging in the cosmological context as the limits on the mass are far below that required to make the neutrino a major mass constituent of the Universe. This leaves us with cold dark matter (CDM). CDM consists of weakly interacting massive particles (WIMPs) that are able to cool and clump together even at relatively high temperatures. This requires the rest mass of most CDM WIMPs to be extremely large. In fact, a typical WIMP would have about 1016 times the rest mass energy of a proton. This is a heavy particle! As discussed in Chapter 3, some WIMPs could have been created very early on through quantum fluctuations and if they did not immediately annihilate with their respective anti-WIMPS, could survive as the dominant relic mass today. The basic problem is that no particle physics experiment on the earth has uncovered any evidence for these WIMPs or any other form of CDM despite searching for more than 20 years. If CDM exists, we are thus quite ignorant about its form. Paradoxically, however, the existence of galaxies may in fact require some form of CDM (see below).

    Structure Formation

    The distribution of galaxies (see Figure 4.8) is very complex. The basic mechanism that we can understand for the formation of structure in the Universe is known as Gravitational Instability. Gravitational Instability works by a relatively simple principle - if there is some density enhancement in a matter field, then that density enhancement will sweep up material and continue to grow. The problem with this scenario occurs if there is no dark matter in the Universe. As discussed in Chapter 3, baryonic material in the Universe would be subject to strong radiation pressure and drag and would have a difficult time clumping. In fact, it's not clear if galaxy formation would even ever occur if only baryons exist. Hence, one of the best physical arguments for dark matter is the very existence of galaxies. Baryonic density fluctuations will likely not produce galaxies. To produce galaxies you need a heavy particle that is not effected by radiation pressure so it can clump and form density enhancements very early on. If this is correct, it means that galaxies are surrounded by dark matter halos which trapped baryonic gas (e.g. hydrogen) and turned it into stars. This also means that there should be some halos which didn't trap any baryonic material to eventually form a luminous galaxy and therefore should remain dark.

    The exact mechanism of how Gravitational Instability actually produced the complex patterns seen in galaxy clustering is unknown. This pattern of galaxy clustering is called large scale structure. By structure we mean the distribution of galaxies, clusters of galaxies and collections of clusters of galaxies known as superclusters. In Figure 4.8 we see a very complicated map of the galaxy distribution. Large filaments or walls are seen as are a number or prominent, quasi-spherical, voids. The overall distribution is quite cellular in nature and some of the observed structures are truly large. In particular, the band of points arcing across Figure 4.8 is known as the Great Wall of galaxies. It seems to be a coherent feature in the galaxy distribution which is hundreds of millions of light years long. The mechanisms that could create such huge, coherent features are quite mysterious.

    Figure 5.7 Large scale structure in a Dark Matter supercomputer simulation. Image courtesy of the HPCC group at the University of Washington and George Lake. This simulation shows a void filled Universe with much filamentary structure. Clusters of galaxies appear to form at the intersections of voids.

    In the study of large scale structure, theory and observations generally are not in good agreement. Several attempts to simulate large scale structure in Supercomputers have been done. Figure 5.7 shows an example of one such simulation. The patterns seen there are striking. There is much filamentary structure and there are large regions where there are no galaxies (these are called voids). The pattern is very much a cellular one in which structures seem to form at the interfaces between the voids. This void filled Universe is qualitatively similar to the real galaxy distribution, another example of which is shown in figure 5.8. Quantitatively however, these simulations generally produce too large of voids and too much filamentary structure. Hence, the details of structure formation remain relatively unknown to us. In simple terms we know that after recombination there were pockets of density enhancements around which material accumulated. What we don't know are the scales involved. In particular, there are two completely different mechanisms which could still produce the highly clustered, void-filled Universe that we observe.

    Figure 5.8: The spatial distribution of 4000 galaxies in a thin slice in the Southern Hemisphere. The volume covered by this slice is significantly larger than that shown in Figure 4.8. However, the same pattern of voids, walls, and shells is clearly present.

    The first mechanism suggests that extremely large objects formed first. This is known as the top-down scenario. These large objects have the mass of several galaxy clusters. Subsequent fragmentation of these very large regions into smaller regions then produced the hierarchical pattern we see today- galaxies in clusters, clusters within superclusters, etc. At the opposite extreme is the scenario which argues that sub-galactic size masses formed first. This is known as the bottom-up scenario. After these sub-galactic masses are formed, subsequent gravitational coalescence produce galaxies, which in turn gravitationally coalesce to produce clusters of galaxies. In some sense, the bottom-up scenario is similar to the accretion process that formed the planets, where tiny grains coalesced to make larger objects until eventually a planet formed.

    Figure 5.9 A Hubble Space Telescope of distant sub-galactic mass objects that appear to be coming together to form a single galaxy.

    Both the top-down and bottom-up scenarios can produce the same kind of large scale structure in the Universe so, even though the physics is much different in these scenarios, observations of the nearby Universe and its associated patterns of galaxy clustering can't really tell us which one occurred. The main difference between these two scenarios is that, in the top-down one we would expect to see clusters of galaxies very early on in the Universe where as in the bottom-up scenario we would expect to see galaxies before we would see them arranged in clusters. Therefore, if we can look farther and farther back in time, we may be able to observationally map out the correct time sequence. Very recent deep space observations with the Hubble Space Telescope (e.g. the Hubble Deep Field) directly show the existence of sub-galactic masses which seem to be coming together to form one galaxy. This evidence is shown in Figure 5.9. This provides good support for the bottom-up scenario but leaves open the general question of the high degree of clustering seen in the Universe. Such clustering, if driven only by gravitational processes, would have a difficult time producing the largest coherent features (e.g. The Great Wall), we see in the galaxy distribution in only a few billion years.

    The Inflationary Paradigm and W = 1

    In the early days (1965-1975) of Big Bang cosmology, when there was little evidence for dark matter, the preferred model was a low density, baryon dominated Universe of age approximately 18 billion years. However, with the evidence presented above about the existence of dark matter, a fundamental alteration of this baryon-dominated cosmological model might be required. In addition, when looked at in detail, the Hot Big Bang model does not naturally predict some aspects of the large scale nature of the Universe. These predictive problems are enumerated below and can be ameliorated with a new twist on the physics of the very early Universe called inflation. Inflation is a very complicated physical theory but its essence is simple: it posits that the Universe we observe today resulted form a very strange phase in the very early Universe in which the the initial expansion epoch was exponential in nature. An exponential increase in the radius of the Universe produces a much larger Universe in a much shorter period of time, than uniform expansion does. This helps to resolve some problems with the standard Big Bang model.

    There are basically three problems that inflation solves and they are known as the Flatness, Horizon and Smoothness problems:

  • The Flatness problem: When the Universe is formed, it can have any value of W that it wants to at later times. W = 1 represents a special case where the Universe is spatially flat. At early times the density of the Universe was enormous and W is very close to 1. This condition is independent of the value of W that we measure today, 10--15 billion years after the expansion. However, the observation that the W we measure today, which is in the broad range of 0.01 -- 1 (i.e. still close to 1 when it could be 106, 10-6, etc) has lead many to suggest that W must be identically one or the Universe would have either re-collapsed long ago or be so under-dense that galaxies would not have formed. A specific value of W today in the range 0.01-1 would imply that the conditions at the present epoch are somehow imprinted on the initial conditions that determine the expansion.

    Inflation makes a simple prediction that W = 1 and the Universe is spatially flat. This is because any initial curvature in the Universe was erased by the enormous expansion caused by inflation. Imagine taking a basketball and then exponentially inflating it so that its radius increased by a factor of approximately 1050 in a few millionths of a second. Any initial curvature is rapidly "inflated" out by the enormous increase in surface area of the basketball so that the final area is flat to essentially one part in 1050. In this manner, the inflationary theory makes a definite prediction about the geometry of the Universe; space must be flat.

  • The Horizon Problem: In an expanding Universe there are particle horizons. The size of these horizons to first order is set by the speed of light and the expansion rate so that rhor ~ cTexp where Texp is the expansion age at some redshift, z . As the Universe ages (expands), the particle horizon increases and more material can come into causal contact with that particle. At early times, individual particle horizons could encompass only a fraction of the volume of the Universe. At the time of recombination when the CMB photons are finally freed from the matter, the angular size of a particle horizon on the sky was about one square degree. Yet over 44,000 square degrees of sky, the CMB photon density is the same. This means the conditions of the Universe are the same in regions that are causally disconnected.

    In the standard Big Bang model, this would require that the initial conditions of the Universe were homogeneous and that would be a very improbable state. Inflation, however, solves this directly. The initial conditions of the Universe could have been very heterogeneous but in each small domain, which was homogeneous, there was an inflationary event. Our observable Universe is just one of many possible domains. You can think about this as follows: look around the environment in which you are reading this book. This environment is very heterogeneous. Now imagine taking a cubic micron of that environment and inflating it by a huge factor so that if fills space and becomes the Universe. There is a high probability that the cubic micron you picked to inflate was homogeneous, even though you picked it out from a very heterogeneous initial state. Thus, the inflationary paradigm directly predicts that the observable Universe will be homogeneous. Without inflation, a special condition would had to exist early on to produce the homogeneous CMB that we observe. Overall, this horizon problem is a pretty strong argument for the inflationary theory.

  • The Smoothness problem: On a large scale the Universe is extraordinarily smooth, as evidenced by the low anisotropy measured by COBE (see Figure 2.8). Yet in this smooth Universe, there exists a high degree of galaxy clustering (Figure 4.8). As argued earlier, it would be difficult to account for this clustering if there was not some form of dark matter present in the early Universe to start the process of structure growth very early on. As a consequence of predicting that spacetime must be spatially flat, inflation then demands a Universe which is dark matter dominated and this helps to solve this problem. In principle, the more dark matter there is, the more structure formation can occur.

    In sum, the inflationary paradigm, while operating via some unknown but clearly fundamental physics, provides some elegant solutions to the problems encountered in the standard Big Bang model which is baryon-mass dominated. Lately, inflation has come under fire because most observations do not indicate that W =1, as predicted. However, inflation only predicts a spatially flat Universe (not a specific value for W). Since the curvature of the Universe is determined by both W and L then inflation predicts that W + L = 1.0. Hence, if we believe the observations that W < 1 and that the inflationary paradigm must hold, we are again driven to considerations of a non-zero L. Einstein's biggest blunder once again, may have instead been another fundamental insight as dynamics of the Universe in this case are now driven by vacuum energy. Resolution of the L issue is one of the most exciting problems in current observational cosmology. If the Cosmological Constant turns out to be real, the Universe will have taken on an added degree of complexity.

    Hidden Galaxies Revealed

    We conclude this chapter by briefly considering another recent discovery that has significantly altered our view of the characteristics of galaxies. We begin by introducing a thought experiment. An important corollary to the Cosmological Principle (see Chapter 2) would assert that all observers in the Universe should construct the same catalogue of galaxies. If this were not the case, then different observers might have biased views and information about 1) the nature of the general galaxy population in the Universe, 2) the three dimensional distribution of galaxies, and 3) the amount of baryonic matter that is contained in galaxies. Thinking about the Cosmological Principle in terms of the homogeneity of observers' catalogues of galaxies raises an immediate and perhaps profound problem which can be stated very simply: If you see (detect) a galaxy you can catalog and classify it; if you don't see it you can't.

    Since galaxies in general are quite diffuse and low contrast objects with respect to the noisy background of the night sky, which has finite brightness, one can easily conceive of observing environments that would make galaxy detection difficult. For instance, suppose that we lived on a planet that was located in the inner regions of an elliptical galaxy. The high stellar density would produce a night sky background that would be relatively bright and therefore not conducive for the discovery of galaxies. Or, consider the poor astronomer that lives on a planet which has two moderate size moons in orbit about it, at least one of which was in the night sky at all times. Such a planet would have no "dark" time and observers would be hard pressed to discover external galaxies.

    Although these are extreme situations, they illustrate the basic point that for all observers, the finite brightness of their night sky acts as a visibility filter which, when convolved with the true population of galaxies, produces the population that appears in catalogs. Thus, we have no guarantee that our location in the outer regions of a spiral galaxy, on a planet with 50% dark time per lunar orbital cycle, allows us to detect and catalog a representative sample of galaxies.

    Improvements in detector technology have now allowed for the discovery of galaxies that have low contrast with respect to the night sky. Some visual examples of surface brightness selection effects are shown below in Figure 5.10. Each of the galaxies here has the same total mass. The galaxy in the upper left part of the Figure (M51) has a very high contrast with respect to the background while the similar mass galaxy in the lower right panel is barely detectable above the noise of the night sky. It is galaxies like this that comprise this new population of hidden galaxies which have now been discovered by astronomers.

    Figure 5.10: Surface Brightness Selection Effects:

    Figure 5.10 Digital images of galaxies with different contrasts with respect to the sky background. Galaxies like those shown in the upper left are easy to detect while galaxies like those in the lower right are considerably more difficult to detect. As the total mass in these galaxies is nearly the same, its clear that hidden, diffuse galaxies can still contain substantial amounts of material.

    These hidden galaxies, despite being as large as our own Galaxy, have escaped detection for many decades because their signal effectively competes with the noise of the night sky background. We are just now beginning to detect these new objects and to study their properties in some detail. While these objects have significantly different properties from more normal spiral and elliptical galaxies, their main interest to us here is in a cosmological context as they provide use additional sites where mass has accumulated but has gone unnoticed. As such, their recovery has essentially increased the mass of the Universe that is contained in galaxies. In fact, the data are consistent with as much mass as in normal galaxies being contained in this newly discovered population. Moreover, there is data which indicates that the M/L ratio of these LSB galaxies is significantly higher than it is for more normal galaxies. If this is indeed the case, then it argues that the majority of the baryonic matter in the Universe in fact, is contained in a population of galaxies that has just been recently discovered.

    While the discovery of LSB galaxies does not solve our overall missing mass problem (there is still ample room for non-baryonic dark matter), it very much serves as a reminder that observational cosmology is still in its infancy and that there are still new things to discover and learn about the Universe. Furthermore, this serves as a reminder about the important role of bias in observational cosmology. For instance, prior to the discovery of this new population of galaxies, galaxy evolutionary theory was thought to be secure. Now we know that we have missed approximately 50% of the general galaxy population so that our previous view was both biased and incomplete. Even now, for instance, most introductory textbooks don't even mention this new population of galaxies (things change slowly ...). Hence, prior to the discovery of LSB galaxies we had a very biased view of the general galaxy population. Its not possible to construct a general evolutionary model based on a biased sample. With the detection of LSBs we have a more representative sample of galaxies and with that sample we have new challenges to our theories. In particular, the properties of LSB galaxies suggest they have very low mass densities compared to normal galaxies and this raises serious questions about how they could have formed in the first place.

    Overall, however, the discovery of LSB galaxies should be gratifying for it is a signature that the Universe still has not revealed all to us and there are still likely to be many more mysteries to encounter in the coming years. Because of that, we should fully expect the cosmology that we have specified here will be subject to great change, perhaps in the very near future.


    In this chapter we have considered some of the complexity in the Universe. The bulk of this chapter has been devoted to a discussion of dark matter, the resolution of which is of profound significance. Simply put, our ignorance as to the nature, distribution and amount of dark matter means we know very little about the basic nature of our Universe. The dark matter problem, however, originates under the assumption that we know the behavior of gravity on very large scales. Thus, one possible resolution is that there is no dark matter and it's our understanding of gravity that is deficient.

    If there is dark matter we are rather unsure of its nature. However, if the Universe is closed, then it's very likely that the dark matter is non-baryonic and in the form of some particle we have not yet discovered. Furthermore, there must be a substantial amount of dark matter distributed between the galaxies. On the other hand, the observational determination that W is in the range 0.1-0.3 is consistent with all the dark matter being located where there are galaxies (i.e in galaxies or in clusters of galaxies). But the form of this dark matter remains unknown. The MACHO observations of our Galactic Halo strongly limits the amount of sub-stellar mass objects that are located there. Similarly, the lack of halo brightening in distant galaxies limits the parent population of luminous stars which could evolve to become stellar remnants.

    Another argument for the existence of dark matter is the complexity observed in the galaxy distribution. Currently the formation of large scale structure in the Universe is not well understood. However, this formation is greatly facilitated if there is some form of dark matter in the early Universe that is able to clump together during the radiation dominated era.

    This chapter also introduced the complex concept of inflation, which is a new twist to the standard Hot Big Bang Theory. The great advantage of the inflationary theory is that the Universe is predicted to be homogeneous. In the standard Big Bang model, homogeneity would have to be an improbable initial condition. Inflation also predicts that space is flat. If inflation is indeed the mechanism that has produced the observed homogeneous Universe and if we believe the data which suggests that W is in the range 0.1 -- 0.3, then the spatial flatness requires L to dominate the energy field in the Universe today. If this is true, then Einstein's "biggest blunder" in reality was one of his greatest triumphs.

    We closed this chapter with a brief discussion about a new population of galaxies that has remained hidden from our view due to their extremely diffuse nature. The discovery of this population is important because it shows that not only has our view of the general galaxy population been severely biased, but that it's possible for the Universe to offer us new objects, never before seen. As a consequence we should expect the cosmological model which has been presented here to be subject to considerable change in just the next few years. As intelligent beings we will continue to be curious and that curiosity will drive innovation in the kinds of instruments and observations that can be made. With new observations comes new insight unless we are encumbered by bias. In many respects, the study of Cosmology is a humbling experience which reminds us that of all that we know, the amount that remains unknown is vast by comparison.