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Title COBE Educational Resources (1993)
Author(s) Alexander Kashlinsky

Note from the editor: Major scientific discoveries were made by each of the three instruments aboard NASA's Cosmic Background Explorer (COBE) satellite, and more can be expected from the planned Microwave Anisotropy Probe (MAP) and Planck missions. Further significant results have come from ground-based, balloon-borne and other space-based observatories. The following essay, by Dr. Alexander Kashlinsky, highlights the COBE findings and provides a context in which the significance of the measurements can be appreciated.

Further discussions of certain topics can be found elsewhere on the World Wide Web by following the hyperlinks, a majority of which lead to sections of Ned Wright's tutorial and the MAP Education and Outreach pages.

Making the Science Exact: Recent Developments in Cosmology

A. Kashlinsky

Cosmology is the study of how the current structures in the Universe came about. Except for some rare and speculative attempts, it does not try to answer how the Universe itself came about but, rather, what were the physical processes that have led to the structure we observe. Once, cosmology was often described as the hunt for two numbers: the rate of expansion (the so-called Hubble constant) and the density parameter Omega (which distinguishes a Universe that will eventually re-collapse from one that will keep expanding forever). This is no longer true. The field has seen tremendous progress in the last 20 years and has by now become as exact as any other field of physics. Theoretical understanding has increased dramatically, and the amount and accuracy of the data coming through are now beyond what was considered possible even 5 years ago.

Most of the time, physicists solve (differential) equations that describe changes in observable quantities (say, temperature or speed) in space and time. These equations are more or less universal for all areas of physics and are typically solved for future times starting from knowledge of the initial state of the system. Cosmology works in a reverse way. We observe the Universe today, and then one has to extrapolate backwards in time to figure out the initial conditions and the past history. This is a different kind of problem and requires different tools.

The Friedman model is generally accepted as an adequate approximation to the global evolution of the Universe. Its Newtonian interpretation is simple: the Universe is homogeneous and expanding in such a way that the expansion velocity of each shell of cosmic fluid is approximately equal to the escape velocity from its surface. Such expansion is called the Hubble law, which states that the relative velocity between any two points is proportional to the distance between them, v Hr, H being the Hubble constant. But one needs Einstein's general theory of relativity to explain the expansion. Galaxies are attached to fixed (so-called comoving) coordinates, much like the dots on an inflating balloon, creating the illusion that they themselves are moving away. The global evolution of such a Universe is analogous to that of a stone thrown upward. If its speed exceeds the escape velocity from Earth, the stone will move away forever and eventually continue its "expansion" without feeling Earth's gravity any more. If the speed is too small, the stone will expand to a maximum height and then fall back to Earth and bounce up again. Similarly, if the gravity of the Universe is strong enough to overcome its expansion, it will reach a maximum size, turn around, and re-collapse to a singularity, ending its current cycle in a Big Crunch, and perhaps starting another expansion cycle. If gravity is too weak, the Universe will continue expanding forever. According to general relativity, space in the presence of matter is curved, and the gravity of the matter determines its geometrical properties. In the former case (re-collapse), the geometry of the Universe is like that of a sphere, and it is "closed." In the latter case (expansion forever), the geometry is like that of a saddle, and it is "open." The intermediate case of precise balance between gravity and escape velocities corresponds to plane geometry, and is "flat." Figure 1 illustrates the three possible geometries. The type of universe we live in depends, then, on the average density and is parameterized by the density parameter Omega, which is the ratio of the average density to that necessary to eventually stop the expansion. If Omega > 1, the Universe is closed, if Omega < 1 it is open, and if Omega = 1, the Universe is flat.

Figure 1 Geometries of flat universe (left), closed or positive curvature universe (middle), and open or negative curvature universe (right). The three cases correspond to Omega equal to, greater than, or less than 1, respectively.

In order to explain bound non-expanding objects (galaxies, clusters of galaxies, stars, and, ultimately, to some degree ourselves) in an expanding universe, one has to postulate the existence of (initially) small density fluctuations imposed on the otherwise homogeneous expanding fluid. The matter within the fluctuations "sees" larger mass, feels a stronger gravitational field than the rest of the Universe, and hence expands at a slower rate. In other words, the density fluctuation grows with respect to the background. In fact, a good description of the evolution of fluctuations is to approximate the fluctuation itself as a mini-universe of a slightly larger density. It will then expand at a slower rate, reach its maximum expansion stage, and collapse to produce compact objects. The order and epoch when this happens depend on the spectrum of the fluctuations - i.e., how the typical amplitude varies with the scale it contains, on the amplitude of the spectrum, on Omega, on the epoch when density fluctuations were introduced, and of what they consisted.

Even though the expansion of galaxies was discovered by Edwin Hubble in the 1930's, the Big Bang theory was really placed beyond reasonable doubt only after the discovery of the microwave background radiation by Penzias and Wilson in 1964. This is the relic radiation left over from the Big Bang itself, and is isotropic. Since the Universe once went through a very hot and very dense phase, this radiation, via its interactions with hot, dense, and opaque plasma, should have thermalized to have a blackbody spectrum. Recent measurement by NASA's Cosmic Background Explorer (COBE) satellite confirmed this to an unprecedented degree with measurements from the Far Infrared Absolute Spectrophotometer (FIRAS) (Figure 2) - few labs will be able to produce such an accurate blackbody spectrum! While the radiation was very hot during early phases, by now it has cooled so much that its peak has (red)shifted into the microwave/radio region of the spectrum.

[Image of FIRAS CMB spectrum]Figure 2 Cosmic microwave background (CMB) spectrum from the COBE FIRAS instrument. The solid curve shows the expected intensity from a single temperature blackbody spectrum, as predicted by the hot Big Bang theory. The FIRAS data were taken at 34 positions equally spaced along this curve. The FIRAS data match the curve so exactly, with error uncertainties less than the width of the blackbody curve, that it is impossible to distinguish the data from the theoretical curve. These precise CMB measurements show that at least 99.994% of the radiant energy of the Universe was released within the first year after the Big Bang itself. The results show that the radiation matches the predictions of the hot Big Bang theory to an extraordinary degree. Credit: NASA's Goddard Space Flight Center and the COBE Science Working Group.

Click on image to display larger version.

The Universe as we see it poses many questions about the physical laws responsible for its structure and evolution. One can envisage many laws that would lead to a very different universe, and some such laws may be even more logical. For example, there is the horizon problem: Why is the Universe homogeneous and why does it have the same appearance on all scales? Signals can propagate only at the speed of light, c, and this defines the so-called horizon, which at any given time t, is just ~ct.  In the past, this horizon was very much smaller than it is today. Thus, what could have been the physical processes that led to different regions of the Universe not causally connected in the past having the same structure? The luminous matter in stars and galaxies can account for only 1 percent of the critical density of the Universe. If that were all the matter there was, it would have been impossible for small density fluctuations to grow and collapse into galaxies at all. Luckily, it has been known for some time from the dynamics of individual galaxies as well as clusters of galaxies that their total mass is about 10 times larger, which means that the total Omegais at least 0.1. Galaxies are surrounded by dark massive halos that contain about 10 times as much mass as the luminous stars. Thus, the question of dark matter arises: What is it made of, why, when, and how much? This, in turn, is related to how big the density of the Universe really is and whether it will re-collapse or continue expanding forever: Is it closed, flat, or open? And last but not least, one would like to understand the origin of density fluctuations.

Until the early 1980's, cosmologists concentrated mainly on the formation of structures out of the evolving density fluctuations in the post-recombination epoch. According to the standard model, the Universe started out of a singularity with infinite density and infinitely high temperature. The earliest time when we can start applying the Einstein equations at least semi-confidently is the so-called Planck era, roughly 10-43 seconds after the Big Bang. Prior to this time, quantum effects in gravity were dominant, and the proper treatment of the Universe's evolution has to await creation of a theory of quantum gravity, one of the still unsolved problems of theoretical physics. As the Universe expanded, matter cooled, and normal particles began to appear out of the primordial soup of energy. At about 1-3 minutes after the Big Bang, the Universe cooled enough for some of the protons (hydrogen nuclei) to fuse with neutrons thus converting about 25 percent of the matter into helium and a small, but significant amount into deuterium or heavy hydrogen. Afterward, matter continued to cool, but also was so tightly coupled to radiation by electron-photon scattering that the Universe was opaque and no growth of fluctuations was possible. When the Universe turned about 105 years old, it cooled enough that electrons and protons recombined into hydrogen atoms. It became transparent, and the microwave background photons began to propagate freely to observers. The epoch of recombination is the earliest stage in the history of the Universe that can be observed and studied through observations with photons. This offers an important tool for studying the early Universe, but also shows the limitations of how far into its infant stage it can be seen.

Since the early 1980's, theoretical cosmology has seen tremendous - albeit, at times, speculative - progress. This led to the creation of a new subfield of astrophysics called astroparticles. As the name suggests, it resulted from a kind of marriage between astrophysics and high-energy (particle) physics, and in a way it happened because the Universe offers the ultimate testing ground for particle physics ideas that cannot be probed with the current (or even the next) generation of accelerators. The most popular of these theories is the so-called inflation theory. According to the standard Big Bang picture, the Universe decelerates in its expansion because gravity is the only force driving its evolution. This leads to the horizon scale increasing linearly with time. However, according to the inflation theory, at early times not long after the Planck era, the Universe consisted of a primordial soup of energy, the so-called fields. It was also inhomogeneous, a more natural initial condition. In the state of equilibrium, the field would be located at the minimum of the well created by its potential (just as any physical system tends to the state with minimal energy). According to current field theories, as the temperature of the Universe decreased, the form of the field potential changed, and its minimum shifted so that the field was no longer sitting at its minimum. The field would then start rolling toward the (new) minimum of the potential well. One can always expect to find a small region (smaller than the horizon scale at the time) where the field is distributed homogeneously. If the roll-over is slow (which sets limits on what the form of the potential can be in order for inflation to work), wonders can happen in that small homogeneous patch. The pressure created by such a field during roll-over is dominated by its potential energy and is equal but opposite in sign to the potential, while its density (energy) is also dominated by the potential but is equal to it and has the same sign. Thus, the so-called equation of state during this process reads: P = -rho. In normal circumstances, the pressure, P, is positive, but during inflation it is negative and large and, therefore, wins over gravity and makes the Universe accelerate and expand exponentially - i.e., inflate.

Several things happen during this inflationary expansion. First, as it expands, the Universe super-cools, and after the field has reached its new minimal potential and starts oscillating near the minimum, it decays into normal particles and photons. This re-heats the Universe, and then the standard Big Bang picture begins to apply. The second thing that happens during inflation is that all length scales (including the present horizon) get stretched exponentially; this means that scales that are not in causal contact today could have been so before inflation (when they were much more compact). The homogeneity and the horizon problem are thus explained by supposing that the entire observable Universe originated from this initial bubble that was inflated. As the field rolls down the potential curve, new fluctuations will appear due to quantum uncertainty effects. These fluctuations have the so-called scale invariant Harrison-Zeldovich spectrum; i.e., the amplitude of energy fluctuations on a given scale is independent of the scale. There are some problems vis-a-vis field theories, however. One can show that, for the density fluctuations produced to be as small as required by the homogeneity of the Universe, the field potential must have a very small coupling constant. Last but not least, inflation predicts that, during this roll-over, the Universe becomes very nearly flat, driving the density parameter Omega very close to 1. All of these are testable predictions.

There are also a few alternative theories. Some are based on the topological defects that can appear in space-time during phase transition(s) in the early Universe. These would lead to exotic first objects such as strings, textures, or domain walls, all of which are defects in the otherwise homogeneous space-time. These serve as the seeds for density fluctuations whose later evolution leads to the observed structures. And last, but not least, low values of Omega can be reconciled with standard inflationary picture if the total density is dominated by the vacuum energy - the so-called cosmological constant Lambda- thereby ensuring that the space-time is flat.

All of these theories make predictions about the present-day Universe that can be checked. The strongest (and perhaps most problematic) prediction of the standard inflationary picture is that the Universe today should be flat to a high accuracy. This makes a prediction on what the dark matter should be made of. The nucleosynthesis calculations (helium, deuterium, and lithium production) set strong limits on what the density in normal, so-called baryonic matter (protons and neutrons) can be. Deuterium cannot be made in significant amounts by any known processes other than the Big Bang, and it is, therefore, a particularly sensitive indicator of the total baryon density. Deuterium abundance measured in the Solar System and now also in interstellar clouds by the Keck and Hubble telescopes implies that the density of baryons can not exceed ~10 percent of the  closure density. This, in turn, means that for inflation to work with the total density of the Universe at the critical value, the dominant bulk of matter in the Universe (~90 percent) must be in some non-baryonic form. One such candidate is  neutrinos, whose number density is known from the theory of weak interactions and the physics of the early Universe. The idea that neutrinos may be massive has recently received support from the Kamiokande measurements of the cosmic ray spectra that measured mass difference between the various neutrino species. The measurements indicated that the difference in masses is about 0.01 eV. This certainly suggests that the neutrino is indeed a massive particle, requiring revision of the standard model of particle physics. On the other hand, for neutrinos to be "minimally" cosmologically important they need to have mass in excess of a few eV, which is significantly larger than their mass difference. In order to make the Universe flat, they then must have mass of about 30 eV (for comparison, the mass of an electron is 500,000 eV), but this hypothesis is not easy to reconcile with the formation of the observed structures. Thus, some physicists speculate that the dominant mass of the Universe is in some new exotic form - the so-called Cold Dark Matter. Many experiments are now underway to detect this hypothetical new matter, and many theories are being put forward that predict the new particles' form, interactions, and masses.

There are several possible ways to measure Omega. The most obvious way is to weigh the matter in the Universe - at least the luminous part of it that is concentrated in galaxies and clusters of galaxies. The dynamics of the latter allows us to determine their masses assuming (quite reasonably) that these systems are in equilibrium between gravity and pressure due to centrifugal forces or random motions. (Note that this is also the way the mass of Earth is determined from the Moon's motion, etc.). Such measurements were pioneered by Zwicky in the 1930's, and have since consistently given a value of Omega = 0.1 - 0.2. This is about 10 times as much as the luminous mass density (so there definitely is dark matter), but a factor of 10 below the critical density so that the dark matter associated with galaxies is not enough to make the Universe flat. Thus, either inflation theory is in trouble, or there must be about 10 times as much matter as we have been able to detect. But where could it be?

Or do we live in a low density Universe whose density is dominated by the vacuum energy component, the cosmological constant Lambda? Indeed support for such a scenario comes from recent measurements of supernovae of type Ia at (high) redshifts out to z ~ 1.  Type Ia supernovae form due to catastrophic nuclear burning by matter falling onto the surfaces of already-formed white dwarf stars. Because white dwarfs have mass specified by the Chandrasekhar limit, 1.44 MSun, these supernovae represent "standard candles," i.e., they all have very similar luminosities at the peak of their explosion, and similar light curves, which describe how the luminosity emitted by the exploding star varies as a function of time since the explosion. Thus, one can derive the distance to a Type Ia supernova from its apparent brightness. Such distances for supernovae at redshifts z > 0.5 are sensitive to the cosmological parameters Omegaand Lambda, enabling measurement of the latter. Several groups have recently detected enough Type Ia supernovae in this range of redshifts to give the first reliable measurements of the cosmological parameters. Although the present-day measurements have large uncertainties, the available data seem to favor a low density Universe dominated by the cosmological constant. If confirmed with future and larger datasets, this would have profound implications for cosmology. It is expected that quantum uncertainty in the state of the early Universe could generate a cosmological constant whose magnitude is comparable to the Planck mass energy. But the data and the fact that the Universe is at least 10 billion years old suggest that the observed value of the cosmological constant is more than 120 orders of magnitude lower than that. So how could it have been generated with values so small, yet different from zero?

The other test of Omega is by measuring the age of the Universe. Obviously, it must be at least as old as the oldest systems it contains. Such systems are thought to be globular clusters of stars for which age determinations make the Universe at least 14 - 17 billion years old. Theoretically, one can predict what the age of the Universe is if one knows H, Omega and Lambda. If Lambda = 0 and gravity is negligible (Omega << 1), there is little deceleration, and the age would be H-1, the so-called Hubble time, but if Omega = 1, the age is decreased by a factor of 2/3. Two recent measurements of H from the Hubble Space Telescope and the Keck telescope on Mauna Kea in Hawaii lead to H-1 ~ 13 billion years. If  Omega = 1, the age implied by this expansion rate would be significantly smaller than the age of globular clusters. Is the Universe open after all? If so, can the inflationary model be modified to account for this? A non-zero positive cosmological constant would also lead to an increase in the age of the Universe for a given value of the Hubble constant (H) and could lead to an age even in excess of the Hubble time, H-1.

The other key test of theories of galaxy formation is the spectrum of density fluctuations and how early in the Universe they were imprinted. As mentioned, one can hope to see only as far as the epoch of recombination. This would still correspond to seeing the Universe when it was only 150,000 years old, or roughly one hundred thousandth of its present age! According to the conventional wisdom, no stars yet existed at that time, but small density fluctuations that were later to lead to galaxies had already been put in place. Microwave background photons last interacted with matter at the onset of recombination and, therefore, should carry memory of what the density in the Universe looked like then. In a seminal paper in 1965, shortly after the discovery of the microwave background, two theoreticians, Sachs and Wolfe, showed that the slightly inhomogeneous gravitational field generated by density fluctuations, if already present then, should lead to very small temperature fluctuations in the microwave background. Their amplitude should be very tiny - about 1 part in 10,000 to 100,000 in the relative temperature differences on scales separated by several degrees (or more) on the sky. Hence, the searches for these anisotropies began very soon after the microwave background was discovered.

Figure 3 Spectra of the Galactic foreground emission components (free-free, synchrotron and dust) and the cosmic microwave background. The COBE DMR bands were strategically located in the region of minimum foreground emission, at 31.5, 53, and 90 GHz. Credit: C. Bennett (see Bennett et al. 1992, Astrophysical Journal, 396, L7).

Click on image to display larger version.

Figure 3 illustrates how difficult it is to measure these anisotropies. The radiation peaks at frequency of about 5 cm-1 or 150 GHz. Since one observes it through the "smog" of our Galaxy, in order to find the tiny fluctuations, one has to eliminate the contributions from the Galaxy to a very high degree of accuracy. The task of measuring anisotropies from the ground is further frustrated by the effects of Earth's atmosphere. Thus, despite persistent attempts, no convincing evidence came for almost three decades. Then, in 1989, NASA launched the COBE satellite with the explicit task of measuring the microwave background sky from above the atmosphere. COBE had three instruments: the above-mentioned FIRAS to measure the spectrum of the microwave background very accurately, the Differential Microwave Radiometers (DMR) to measure the anisotropies, and the COBE DMR was designed to operate in the range of wavelengths where the foregrounds, coming from the free-free and synchrotron emission at short frequencies and from Galactic dust at long frequencies, have minimal pollution. In April 1992, at the American Physical Society meeting in Washington, DC, the COBE team announced the discovery of anisotropies at the level of about 1 part in 100,000 on a scale of a few degrees. The angular spectrum of the anisotropies is consistent with the inflationary theory, but within uncertainties it is also consistent with the predictions of its competitors. Figure 4 shows the microwave background sky as seen by the DMR. What was measured and is shown is nothing less than the entire observable Universe when it was only approximately 105 years old.

[Image of DMR data]Figure 4 This false-color image shows tiny variations in the intensity of the cosmic microwave background measured in four years of observations by the DMR instrument on NASA's COBE satellite. The blue and red spots correspond to regions of greater or lesser density in the early Universe. These "fossilized" relics record the distribution of matter and energy in the early Universe before the matter became organized into stars and galaxies. The features traced in this map stretch across the visible Universe: the largest features seen by optical telescopes, such as the "Great Wall" of galaxies, would fit neatly within the smallest feature in this map. Credit: NASA's Goddard Space Flight Center and the COBE Science Working Group.

Click on image to display larger version.

The third COBE instrument - DIRBE - detected the Cosmic Infrared Background (CIB) at wavelengths of 140 and 240 µm (micrometers), and set limits to the CIB brightness at eight other infrared wavelengths ranging from 1.25 to 100 µm. CIB emission was also seen at the highest frequencies observed in the COBE FIRAS spectra, providing independent confirmation of the DIRBE result. The (high) levels of the cosmic infrared background at long infrared wavelengths are probably indicative of early galaxy formation and efficient dust production in high-redshift galaxies. These results have profound implications for cosmology and the physics of galaxy formation. As illustrated in Figure 5, foreground infrared emission from the solar system (zodiacal light) and the Milky Way had to be modeled accurately and subtracted from the observed sky brightness in order to find the cosmic infrared background.

Figure 5 Cosmic Infrared Background emission was detected in data from the COBE Diffuse Infrared Background Experiment. The map at the top is a false-color image showing the observed infrared sky brightness at wavelengths of 60 (blue), 100 (green) and 240 µm (red). The bright white-yellow horizontal band across the middle of the image corresponds to emission from interstellar dust in the plane of our Milky Way Galaxy (the center of the Galaxy lies at the center of the map). The red regions above and below this bright band are "infrared cirrus" clouds, wispy clouds of relatively cool Galactic dust. The blue S-shaped figure follows the ecliptic plane and represents emission from interplanetary dust in the solar system. The map in the middle is a 60-100-240 µm false-color image depicting the sky after the foreground glow of the interplanetary dust has been modeled and subtracted; this image is dominated by emission from interstellar dust in the Milky Way. After the infrared light from our solar system and Galaxy has been removed, what remains is a uniform Cosmic Infrared Background. This is illustrated in the bottom image, which shows just the residual 240 µm brightness. The line across the center is an artifact from removal of the Galactic light. Credit: STScI OPO - PRC98-01; M. Hauser and NASA.

Click on image to display larger version.

Last but not least, the recent years have seen a dramatic observational breakthrough that can perhaps offer a clue to the nature of dark matter. As mentioned, the only place we know that dark matter should definitely exist is in the galactic halos, including the halo of our Galaxy. This dark matter can consist either of elementary particles (neutrinos, cold dark matter) or dark astronomical objects. These objects can either have a very low (sub-stellar) mass of ~0.1 solar masses, in which case they are called brown dwarfs or "Jupiters," or be massive black holes. From Galactic dynamics, we know that if they are very massive, their mass must be less than about 106 solar masses, because more massive objects would sink to the center of our Galaxy in less than its age due to dynamical friction, contrary to what is observed. But what if they are low-mass "Jupiters"? In this case, micro-lensing can offer a way to find these objects if dark matter is composed largely of them. According to general relativity, a gravitating body deflects light and acts like an optical lens. Then, because of the focusing, it leads to greater luminosity of the lensed object (more photons are now focused on the observer). Suppose now that we are looking at stars in other galaxies through the halo of our own. Because any Jupiters in the halo must be moving (just like stars in the galaxies), every now and then they would pass between the monitored star and us, resulting in a sudden flare-up in the apparent brightness of the background star. From the intensity and duration of the flash, one can derive the mass of the passing dark object. Such events should be very rare for any given star, but if the halo contains many Jupiters, then by monitoring a few million stars in the Small and Large Magellanic Clouds, which are satellites of our Galaxy, one expects to see several such events per year. Two things distinguish such amplification from intrinsic variability. First, the detected event must be achromatic, i.e. wavelength independent. Second, the flash must be strictly symmetrical in time. Three groups of collaborating astronomers and particle physicists have now discovered such events. One, dubbed the "Gold Plated Event," was caused by an object whose mass is about one-tenth that of the Sun. Could it be that dark matter is composed predominantly of "Jupiters" as the most recent analysis of the combined data seems to suggest? Time will tell.


[Blue bullet] COBE Educational Resources
[Blue bullet] COBE Home Page

NASA Rep. and editor David Leisawitz, leisawitz@stars.gsfc.nasa.gov
Last Revised 25 August 1998