by George Rhee
The brightness of the cosmic background radiation depends on the direction one is looking. These changes in intensity with small changes in direction reveal the first clumping of matter after the Big Bang, the seeds of galaxies. The cosmic background effectively carries with it an image of the universe when it was only 400,000 years old. To detect these galaxy seeds NASA decided to build a satellite. There was a strong motivation to detect the predicted brightness variations. Lack of detection would have meant that galaxies did not form by the gravitational collapse of slightly overdense regions in the early universe.
The Cosmic Background Explorer Satellite: NASA’s Triumph
The COBE satellite discovered the primordial density fluctuations that formed the large structures such as the Sloan great wall of galaxies. When the results were presented at the annual meeting of the American Astronomical Society there was a standing ovation. Three instruments were on board the satellite; a spectrograph designed to measure the spectrum of the background to high accuracy, a radiometer designed to map the cosmic radiation, and an infrared experiment designed to search for the cosmic infrared background radiation.
The radiometer was designed to operate at wavelengths where the contamination from our galaxy is minimal. The radiometer detected the variation in the intensity of the background as shown in Fig. 7.2. The amount of variation was found to be at a level of one part in 100,000. Studies of the early universe moved from speculations to theories that could be tested with actual measurements. The whole field of cosmology changed.
Fig. 7.2The sky images from the COBE satellite differential microwave radiometer. Each map shows the information from the whole sky much as we can show a map of the spherical earth on a page. The top map shows all of the information. This map is dominated by an effect called the dipole, caused by the motion of our galaxy relative to the background radiation. In the middle map the dipole effect has been removed leaving the cosmic background emission and the emission from our Milky Way Galaxy. The emission from our galaxy is the broad horizontal strip in the middle. In the bottom image only the variations in brightness due to the cosmic background radiation remain. These variations are very small (Credit: NASA)
The satellite orbited the Earth 14 times a day. The infrared instruments were kept cool using 650 l of liquid helium. These instruments had to be kept cool to prevent them from emitting infrared radiation. Twenty four hours worth of data could be transmitted to the ground and stored in 9 min. COBE was funded as part of NASA’s Explorer mission program, it had a relatively small cost of 30 million dollars, less than we spend each morning in the war in Afghanistan. COBE triumphed because it held the only route to observing the cosmic background fluctuations.
How do we know that the background radiation is indeed of cosmological origin? Fred Hoyle and others used to argue that the radiation is produced by starlight scattered by iron needles. These scientists did not believe that a Big Bang took place, so they needed an alternative explanation for the existence of the microwave background. Such needles could be produced in the wake of supernova explosions, which are known to produce iron. There are two problems with this idea. First, it is very difficult even in the laboratory to produce blackbody radiation that follows the theoretical curve as precisely as the observed background does (Fig. 7.3). It is hard to imagine how iron needles would do the trick. They would have to be heated by starlight which is not at a uniform temperature, nor homogeneously distributed in space. Needles produced in supernova explosions would be distributed like stars which are not at all homogeneously distributed around us. The Big Bang, as unlikely as it may seem, is the only plausible mechanism we have come up with to account for the background radiation.
Fig. 7.3This figure depicts space as a grid. Our location in the universe is depicted as the red point. The circle depicts our horizon which is how far into space we can see (upper left panel). The radius of the circle is determined by the time elapsed since the Big Bang. Shortly after the Big Bang this radius is relatively small. We have depicted an event, say a supernova going off at this time, as a green dot. The event is located three by three grid cells away. The panel b shows that after some time space has expanded and the light from the event has traveled outward in all directions (green dashed circle). When the light from the event finally reaches us as shown by the green dashed line reaching the red dot we observe the event with our telescopes (panel c)
A good test would be to measure the radiation temperature at high redshift. When the universe was younger the background radiation would have had a higher temperature. In 1994, astronomers used the Keck telescope to study absorption lines of carbon in gas clouds close to a quasar at redshift 1.8. One cloud has a measured temperature of 10.4 K while the other has a temperature of 7.4 K. The predicted temperature of the background radiation at redshift 1.8 is about 7.6 K. The measured temperatures have errors of about 1 ∘ or so. The agreement is fairly good but not perfect. The interpretation of the data is complicated by effects of molecular collisions in the clouds. The measurements do confirm that the temperature was higher in the past.
The Journey of Light Through the Expanding Universe
After neutral atoms form, the light from the Big Bang starts on its long journey through space until some of it is caught by our telescopes. Figure 7.3 shows three snapshots of light propagating in an expanding universe. The grid marks the location of points that are taking part in the expansion. In the upper left panel an event takes place such as a supernova explosion. Our location is marked by a red dot. The cosmic (or Hubble) expansion takes the red and green dots further from each other. The small red circle in the upper left panel shows our horizon; the part of the universe that we can see at any given time. Our horizon expands until it reaches the green dot in the third panel. At that time we can see the event, that is to say the pulse of light has finally reached us.
Figure 7.4 illustrates the fact that events that took place simultaneously at similar distances from us are observed simultaneously. It is a generalization of Fig. 7.3 to multiple events. In the two dimensional case shown in Fig. 7.4 events which took place at the same time in the past are located on a circle centered on our location. In the three dimensional world this circle is actually a sphere. The event for the cosmic background radiation is the point at which the universe became neutral and thus transparent and light could travel freely. The formation of hydrogen atoms occurred everywhere at the same time because it only depends on the temperature of the background radiation. When we observe the cosmic background radiation we are seeing in some sense a snapshot of the surface of a sphere surrounding us. The background radiation conveys direct information about the state of the universe about 400,000 years after the Big Bang. The surface that we see with the cosmic background is known as the surface of last scattering. We experience the same thing when we look at clouds in the sky. We cannot see inside the clouds but we can see the edge of the clouds where light is no longer scattered and can make its way directly to us (Fig. 7.5).
Fig. 7.4 Left panel: all events that happened simultaneously on the blue dashed circle are observed simultaneously. Right panel: the green circle shows the location in space of points we can observe today as they appeared about 8 billion years after the Big Bang (redshift 1). The blue circle shows the location of points that we can observe as they appeared 380,000 years after the Big Bang (the cosmic background) or a redshift of 1,100. The red circle shows the location of points that emitted light at the moment of the Big Bang
Fig. 7.5We can compare our observations of the cosmic background radiation to observations of clouds. When we look up at clouds we see their surface where they become transparent but we cannot look further inside the cloud (Credit: NASA/WMAP Science Team)
COBE’s Successor: The Wilkinson Microwave Anisotropy Probe
The WMAP satellite was designed to carry out detailed measurements of the brightness variations found by COBE. By analogy with Fig. 7.5 it was as if we had discovered the e
xistence of clouds high in the sky and we now wanted to learn about the nature of these clouds by mapping their structure in detail. As we shall see the detailed maps contain a wealth of information.
We can associate a size with brightness measurements. It is as if we were measuring the population of country by laying a grid with a separation of 200 miles between grid lines on a map and counting the number of people in each square. This grid would reveal the most general pattern of population; more people on the coasts less in the Midwest. By moving the grid lines closer together, say 10 miles, we can get much more information revealing the presence of towns and cities, since some squares will have hundreds of thousands of people while others will be at zero. We can then estimate the variations in the numbers in the squares for a given square size. The variations will be largest for a grid size that corresponds to some real feature such as the size of a city.
This was the idea behind mapping the cosmic background radiation in more detail. The theory predicted that for certain scales (angles in the sky) the variations in brightness should be larger than others. In particular the prediction was that the variations in brightness should be relatively large if one observed the sky with a ‘grid size’ of about 1 ∘ (about twice the diameter of the full Moon). Measurable effects weret also predicted for smaller grid sizes.
The search for these effects was initially carried out using measurements made from balloons. They scanned small patches of the sky but with greater angular detail than could be seen by COBE. The balloon data showed the presence of the main predicted feature on a scale of 1 ∘ but also the presence of a second and third one on scales smaller than 1 ∘ .
In 2001 the WMAP satellite was launched. It measured the entire cosmic background sky at five frequencies. Figure 7.6 illustrates how WMAP revealed the background radiation in much more detail than COBE did. WMAP detected features as small as one fifth of a degree in the sky (about one third of a moon diameter). This is about 30 times more detail than could be seen with COBE.
Fig. 7.6The COBE satellite (upper left) made the first measurements of temperature differences in the cosmic microwave background. The BOOMERANG (middle) and MAXIMA balloon experiments mapped smaller portions of the sky but at much higher resolution. With the WMAP satellite’s high-resolution map of the whole CMB sky (lower right), high precision measurements of the age, density, and curvature of the universe became possible for the first time (Credit: NASA, the National Science Foundation, and Lawrence Berkeley National Laboratory)
Scientists used the WMAP data to measure several numbers of fundamental significance to cosmology; the curvature of space, the baryon (atomic) density, the dark matter density and the dark energy density. All these numbers have been measured to an unprecedented accuracy of 1% or better. WMAP ushered in the age of precision cosmology. How then was this detailed information extracted from the WMAP data?
The Music of the Big Bang
Photons that find themselves in a high density region when the universe becomes transparent will have to climb out of that region to reach us. Just as it costs a rocket energy to escape from the Earth’s gravity, it costs a photon energy to escape the gravitational field of a dense region of the universe. The result is that the photon acquires an initial redshift right at the beginning of its journey towards our telescopes. This photon, in comparison with a photon that started its journey from a place of average density, will have a slightly longer wavelength by the time it reaches us. This gravitational redshift is a small addition to the dominant effect which is the cosmological redshift due to the expansion of the universe.
When matter is still in the form of free electrons and protons, dark matter can compress baryons and radiation from one place to the next, resulting in temperature variations at a redshift. This is because the baryons feel the gravity of a dark matter clump and start falling towards the center of the clump but they feel a pressure from the photons that counters the force of gravity and pushes the matter outwards. What results is an oscillation, a bouncing back and forth, not dissimilar to a weight on a spring, that can bounce up and down. So some of the photons are compressed and at slightly higher temperature and some are at slightly lower temperature depending on whether the photons have over-expanded. When the universe turns neutral, the effect stops because photons then travel freely through space.
Clumps of different size oscillate at different speeds in a plasma. The strongest observable effect comes from large clumps in which the plasma has just had time to be compressed once before neutral atoms form. For smaller clumps the plasma can get compressed and bounce back. Maps of the cosmic background contain the frozen imprint of these plasma sound waves. In this sense we can see the music of the Big Bang.
Fig. 7.7The size of brightness variations in the cosmic background radiation as measured by the WMAP satellite. The largest variations occur at a size close to a degree, twice the size of the full Moon. This is because this is where the plasma waves have their largest effect on the radiation. Also at scales (angles) smaller than this fluctuations get washed out (see Fig. 7.9)
How do we see these sound waves? We measure the brightness variations of the background radiation over the whole sky at small and large angles. This is like measuring the height of small wavelength and large wavelength waves on the ocean. To do this we smooth the radiation map (Fig. 7.6) and then measure the brightness variations. The smoothing erases all the brightness variations smaller than the smoothing size. We can do this from large angles (up to 90 ∘ ) down to quite small angles 0.2 ∘ . For reference the full Moon diameter is about 0.5 ∘ .
Figure 7.7 illustrates this. We can theoretically predict the physical size of the first peak. The angular size in the sky of an object of known size and known redshift depends on the geometry
Fig. 7.8The density of the universe determines its geometry. If the density of the universe exceeds the critical density, then the geometry of space is closed and positively curved like the surface of a sphere. We use the number Ω to characterize the density of the universe measured in the units of a critical density. If the density of the universe is less than the critical density, then the geometry of space is open, negatively curved like the surface of a saddle. If the density of the universe exactly equals the critical density, then the geometry of the universe is flat like a sheet of paper. The WMAP measurements of the angular size of the first peak in Fig. 7.7 show that we live in a flat Ω = 1 universe (Credit: NASA/WMAP Science Team)
of space. The conclusion is that the geometry of space is flat like the surface of a table, rather than curved like the surface of a sphere such as the Earth. If the curvature of space had been found to be positive like a sphere, the angular size of the first peak in Fig. 7.7 would have been found to be larger, on the other hand if the curvature had been negative like the middle figure in Fig. 7.8 the angular size would have been observed to be smaller. The fact
Fig. 7.9Recombination does not happen instantaneously so the last scattering surface has a finite thickness (labeled d in the figure). As a result of this, fluctuations (variations in temperature) on scales smaller than d are washed out which causes us to observe smaller variations in brightness on the sky at small angle separations. This effect is known as diffusion damping. The effect on the measured spatial variations in the background intensity is shown by the blue line in the figure on the right
that the universe has a flat geometry means we can combine the cosmic background and supernova data to determine the relative percentage of dark energy and dark matter in the universe. It turns out that dark energy accounts for 72% of the energy density of the universe. A geometrically flat universe can recollapse eventually or expand forever. The data indicate that our universe will expand forever and that the expansion rate will accelerate.
The formation of neutral atoms did not occur instantaneously. To use our cloud analogy from Fig. 7.5, we can see just a little bit inside the cloud because it does not instantly become opaque like
a price of wood and we can indeed see a little ways inside the surface of last scattering. This has the consequence that the smaller angled variations in brightness get smoothed out as illustrated in Fig. 7.9. This explains why the first peak is so much more pronounced than the second and third ones.
The Parameters of the Universe
WMAP tells us that the universe has flat geometry. The supernova data prove the existence of dark energy. By combining these two results with galaxy data we can calculate with good precision the relative amounts of matter and dark energy in the universe. We do not at this time understand the origin of dark energy or the nature of the dark matter. The three sets of measurements (WMAP, supernovae and galaxies) each enable us to roughly estimate these parameters but when we combine all three measurements the range of possible values is narrowed down considerably. Figure 7.10 illustrates this. The blue ellipse represents the range of values allowed by the supernova data. The orange area represents the region allowed by the WMAP data. The orange area lies quite close to the black line which represents a flat universe as we explained earlier. In fact the overlap between the supernova data constraints (blue ellipse) and the WMAP data (orange triangle) leaves the smaller grey region. This region corresponds to a flat universe. The grey ellipse lies in a part of the diagram well above the red line that separates an accelerating expansion rate from a decelerating expansion rate. The geometry of the universe is flat and the universe is expanding at an increasing rate due to the presence of a mysterious dark energy that currently account for 72% of the density of the universe, the remaining 28% consisting of cold dark matter and baryons. The baryons only account for 4.6% of the density of the universe today. The age of the universe according to WMAP data is 13.73 billion years. These numbers characterize the weight, shape and fate of the universe.
