Matthew Hedman. American Scientist. Volume 93, Issue 3. May/Jun 2005.
In the summer of 2002, a team of astronomers working with an instrument at the South Pole, called the Degree Angular Scale Interferometer (DASI), made an announcement to a packed auditorium in downtown Chicago. These scientists had discovered that the afterglow of the Big Bang, the cosmic microwave background radiation, or CMB, is slightly polarized-the electric fields in these microwaves are preferentially oriented. In other words, this signal from deep space has a direction associated with it-just like the directions associated with signals from radio stations that influence the reception of an antenna with a particular orientation. At the time, I had been working on efforts to measure this elusive signal for about five years as a graduate student and a research fellow, and I was extremely excited to be sitting in the audience for this important event. I knew this discovery opened a new window to the early universe.
Much work still needs to be done before the polarized part of the CMB will give up all of its secrets. The polarized component is, at best, 100,000 times smaller than the unpolarized portion of the CMB, so it is very difficult to measure and requires great patience and attention to detail. There is so much to be gained, however, that several teams of scientists are now attempting to refine their estimates. Here I review the current understanding of how the CMB became polarized and what the measurements might reveal about the universe during its infancy.
For the first few hundred thousand years after the Big Bang, the universe was filled with a hot plasma, a gaseous sea of charged particles. Mixed in were particles of light, or photons. The photons themselves could not travel very far within the primordial plasma before they were scattered by electrons, which, in the searing heat, were free of their usual ties to protons. This scattering of photons meant that the universe was not transparent to light.
As the universe expanded, the plasma cooled as it spread over an increasingly larger volume. When the temperature of the universe dropped to several thousand kelvins, the protons and electrons recombined to form neutral hydrogen atoms, and the photons were set free to travel through the cosmos. This decoupling (of matter from radiation) happened when the universe was merely 300,000 years old.
Now, 13.7 billion years later, these photons are still traveling through the universe. However, their wavelengths have steadily increased as the universe has expanded, so today the cosmos is immersed in a weak bath of microwave photons-the CMB radiation. The CMB is present everywhere in the sky, but people cannot feel or see this radiation because it is very faint, nearly a billion times weaker than the microwaves required to pop a bag of popcorn. Feeble though they may be, these primeval microwaves contain some of the most important information available about the early universe.
Fortunately, specialized devices can map the detailed features in the CMB. For the most part, the CMB appears the same, or isotropic, wherever one looks. But very sensitive instruments such as DASI can measure slight differences, or anisotropies, in the brightness and polarization of the radiation coming from different points on the sky. The fact that such anisotropies exist at all suggests that the plasma in the early universe was not perfectly uniform.
These anisotropies of brightness and polarization were caused by different phenomena in the primordial plasma, and therefore both contain separate clues about the nature of the early universe. The brightness variations that we see in the CMB reflect differences in the density of the primordial plasma. This is because a compressed plasma has a higher temperature and glows more brightly. Measurements of the brightness anisotropies, such as those made in 2003 by the Wilkinson Microwave Anisotropy Probe (WMAP), provide powerful constraints on the structure and composition of the early universe. On the other hand, the anisotropic polarization of the CMB contains information about the dynamics of the early universe, such as the movement of material in the primordial plasma and the number of gravitational waves.
Acquiring a Sense of Direction
The polarization of the CMB was generated in the primordial plasma by the interaction between the photons and the free electrons, a phenomenon called Thomson scattering. When light (which, it must be remembered, is an electromagnetic wave) shines on an electron, the oscillating electric field in the wave causes the charged particle to oscillate in the plane perpendicular to the direction of the incident photon’s motion. In turn, the oscillating electron generates a new electromagnetic wave-it emits light. This light is polarized along the direction of the electron’s acceleration and thus will be polarized in the plane of its motion. So even if the incident light wave is unpolarized, the scattered light can have a polarized component.
The electrons in a plasma have light shining on them from every direction. If the (unpolarized) incident light falling on an electron is equally bright in all directions, the particle will be pushed about every which way. Because the electron moves equally in all planes, the scattered light has no average polarization. However, if the incident light is brighter along one axis than it is along any other axis, the electron will move more in one plane than any other, and the emitted radiation will be linearly polarized. Incident light that varies in brightness in this way is said to have a quadrupole moment. Thus a quadrupole moment in the brightness of the incident radiation generates a polarized component in the scattered radiation.
There are two different mechanisms that can generate local quadrupole moments: bulk plasma flows and gravitational waves. To see how the bulk motion of a plasma can generate a polarized signal, imagine that the plasma is flowing radially toward some point and that there is a gradient in the velocity of the flow. If you switch your frame of reference to that of a single electron, the surrounding plasma appears to be moving toward you from all directions. Now, because the plasma is moving at high speeds, certain relativistic phenomena come into play. For example, a chunk of plasma moving toward you appears somewhat brighter than a chunk of plasma that is not moving. The faster the plasma moves, the brighter it appears. Because the material moving toward you from the front or behind is closing in at a faster speed than the material moving in from the sides, there is a quadrupole moment in the intensity of the radiation incident on the electron. Consequently, the light scattered by the electron will have a polarized component. In this way, variations in the velocity of the plasma give rise to polarized emissions from the plasma.
Such bulk motions of a plasma can be studied in a laboratory, but gravitational waves are a much more exotic way to generate quadrupole moments in a plasma. These waves are freely propagating distortions in spacetime, which are predicted by Einstein’s theory of general relativity. When a gravitational wave passes by, space is alternately stretched and squashed along two orthogonal directions. Photons that happen to be propagating in, say, a vertical direction are squashed together, whereas those propagating horizontally are stretched apart. So the light moving in the two orthogonal directions will have different brightnesses-and a quadrupole moment. When this light strikes an electron, it will emit a polarized light wave.
Flows versus Waves
The bulk motion of material in the early universe should have a close connection to the variations in the density of the primordial plasma, simply because the way that material moves affects where it goes. In contrast, the presence or absence of gravitational waves in the early universe depends on poorly understood events that took place a tiny fraction of a nanosecond after the Big Bang. Thus one polarized signal (that from the flowing plasma) must be consistent with the brightness observations (which reflect density variations), whereas another signal (from the gravitational waves) needs to be measured to see if it exists at all. As it happens, we can do both of these things because the bulk flows and the gravitational waves produce polarized signals with distinct signatures on the sky.
In principle, there are several different sorts of patterns in the polarized signals that could be observed. Patterns that are unchanged under mirror reflection are called E-modes, whereas those that do change under reflection are called B-modes. The bulk motion of the plasma cannot generate B-modes, which would require convoluted circulating flows that should not have existed in the primordial plasma. By contrast, gravitational waves generate both E-mode and B-mode patterns with the same efficiency. Therefore astronomers can distinguish these two sources by quantifying the size of the signals in the E-mode and B-mode patterns. Because the polarization arising from bulk motion is bound to be much stronger than that coming from any gravitational waves, E-mode patterns effectively measure the ebb and flow of the primordial plasma, whereas B-mode patterns illuminate the stretching and squeezing of spacetime.
In reality the signals from bulk flows and gravitational waves will not be so simple to separate. Various things have happened to the photons in the course of their 13.7 billion-year journey through the universe, and some of these goings-on could contaminate the data. It is still unclear whether these phenomena will prevent astronomers from detecting the gravitational waves.
The CMB is a powerful probe of the early universe not only because the variations in the brightness and polarization of the CMB are directly related to the density, movement and gravitational-wave content of the primordial plasma, but also because the properties and dynamics of the 300,000-year-old universe are less complicated than those of other astrophysical systems like spiral galaxies. This simplicity can be seen quite clearly in the map of the CMB-brightness variations produced by the WMAP, which shows hot and cold spots of various sizes and shapes, but no distinctive structures like arcs or spiral arms.
These variations are comparatively easy to quantify and analyze because even though there are hot and cold spots on a wide range of scales, the magnitudes of the variations themselves are tiny. The brightness varies by about one part in 10,000, and the polarization is an order of magnitude smaller. This means that the variations in the density and movement of the plasma were similarly small. Although the faintness of the variations makes them difficult to detect, it allows scientists to simplify the equations that describe how the primordial plasma moved. In particular, it turns out that the variations on one scale did not affect the other scales. We can therefore consider variations on any given scale independently, pretending that the others did not exist.
The variations in the CMB are often illustrated using a power spectrum, a plot showing the magnitude of the variations as a function of scale, Predictions from the cosmological models and the data from the experiments reveal several features, each of which are caused by different physical processes. To get a sense of these processes, let us consider a variation at a single scale in which the density of the primordial plasma varies with position like a simple sine wave. The amplitude of the fluctuation-the difference in density between the most dense and least dense regions-will change with time under the influence of two forces: pressure and gravity. Gravity tends to pull material into regions where there is more material, which will increase the magnitude of the density variation. Pressure acts in the opposite direction, driving material out of dense regions and reducing the size of the density difference.
The effects of these two forces are strongly influenced by the scale of the fluctuation because the universe at any given point in time contains an intrinsic length scale called the horizon scale, which is the distance that light could have traveled in the time since the Big Bang. If the wavelength of the fluctuation is much greater than the horizon scale, the universe looks roughly homogeneous to any electron in the plasma, and the plasma has no inclination to move. But if the wavelength of the fluctuation is much smaller than the horizon scale, the electrons can “see” regions of different densities, and they are subject to forces pushing them toward more dense regions (gravity) or towards less dense regions (pressure). Hence variations on scales greater than the horizon scale do not change much with time, whereas smaller variations can evolve as the plasma moves in response to pressure and gravitational forces.
The horizon scale grew as the universe expanded, so at decoupling-the moment when the CMB photons were released from the primordial plasma-it was smaller than it is now. The CMB therefore carries information about variations both smaller and larger than the horizon scale. Because variations larger than the horizon scale did not change much from their initial state, they are interesting for investigating features of the extremely early universe. Indeed, it is on these large scales that the polarization from gravitational waves will be most detectable. However, because the plasma did not have much inclination to move on these scales, the polarization caused by bulk flows in the plasma is very small.
Variations on scales shorter than the horizon scale at decoupling changed from their initial state when the horizon scale grew larger than the wavelength of the fluctuation. At this time, regions of different densities were in contact, and the plasma moved around in response to both gravity and pressure before the photons decoupled from the plasma. These scales therefore provide information about the dynamic properties of the plasma, such as its mass density and sound speed, which depend strongly on the composition of the early universe.
The competition between gravitational forces and pressure causes the plasma to oscillate in and out of the dense regions. These oscillations change the size of the brightness variations and generate significant polarization through bulk motions of the plasma, producing a series of peaks and troughs in the power spectra. There is a simple and direct relation between the variations in the velocity and the density of an oscillating plasma that is analogous to the relation between the position and velocity of an oscillating mass on a spring. Consequently the variations in the polarization and brightness of the CMB are tightly coupled to each other on these scales.
The variations in the CMB underwent further modifications during and after the decoupling event, which was not an instantaneous process. As it took place, photons traveled finite distances between scattering events, and so wiped out any variations on shorter length scales. After decoupling, some of the photons were scattered by tenuous plasmas produced by stars and other luminous objects, and other photons were deflected slightly as they passed by massive objects. These phenomena alter the polarized signals on both very large and very small scales in characteristic ways and enable observations of the CMB to constrain certain characteristics of the universe after decoupling.
Although the physics that determine the structures and features of the primordial plasma depend on the length scale of the variations, astronomers measure these variations in terms of an angular scale on the sky. The photons have been streaming toward us since decoupling, so they appear to originate from a spherical shell that is centered on the Earth. Thus the angular scales on the sky are essentially proportional to the length scales in the early universe. If the universe were not expanding and had simple Euclidean geometry, the proportionality constant would be determined by the radius of the shell. However, the universe has expanded while the photons were in transit, and the geometry of the universe may not be exactly Euclidean, so the angular scale of features in the CMB also depends on the expansion history and the geometry of the universe.
Although WMAP and other experiments now observe and measure many features in the power spectrum of the brightness variations, astronomers have only just begun to scratch the surface of the CMB polarization. The polarimetry data lack sufficient precision to show clearly the predicted patterns or demonstrate conclusively that the brightness data are consistent with the expected polarization. Moreover, no one has yet detected the elusive signal from gravitational waves.
Measuring the Polarization
Scientists are using a variety of procedures to extract the tiny polarized signal from the relatively huge amounts of unpolarized radiation. These different approaches will all have their own unique strengths and challenges, but all of the methods share certain basic characteristics.
Every one of the techniques measures the difference in the strength of the electric field along two orthogonal axes. Differential measurements are natural in polarimetry, and they are particularly useful in this context because subtracting the two orthogonal signals ideally cancels out the unpolarized component. However, because the polarized signals are extremely small, we cannot be sure that the difference in the response of the instrument is not caused by some asymmetry in the apparatus. Periodically rotating the equipment would allow such discrepancies to be separated from any real signal from the sky. In practice, rotating the entire apparatus is often difficult to do, so a variety of clever techniques are used to modulate the incoming polarized radiation and to isolate the real signals from instrumental artifacts.
Scientists must also be extremely patient because the signal is too small to be measured quickly. Only a finite number of photons can be collected every second, and the signal is typically overwhelmed by random fluctuations in the polarization. Thus the measurement must be repeated over many seconds so that these random variations average out, leaving only the real polarized signals. Even with the best instruments it takes hours to detect the dominant signal from the bulk motion of the primordial plasma. Characterizing the polarization and detecting the primordial gravitational waves will require observing times on the order of years.
Various research groups are now building large arrays of polarimeters to expedite the observations. Because a hundred polarimeters can see in one day what would take a single detector a hundred days, these arrays will be powerful tools for studying the primordial polarization when they begin operation over the next few years.
The CMB is not the only source of polarized microwaves. Electrons and dust inside our galaxy and in extragalactic objects also produce polarized radiation at the CMB wavelengths. Even though these polarized signals may be weak, it is still not clear that they can be ignored, especially when it comes to detecting the faint gravitational-wave signal. Fortunately, the frequency spectra of these other sources are very different from that of the CMB, and so astronomers plan to measure the cosmological polarization at several wavelengths. These observations should allow scientists to identify the foreground signals and to isolate them from signals with a cosmological source.
Attempts to measure the polarization of the CMB have a long and difficult road ahead, but there has been good progress. Just last September several experimental groups-DASI, the Cosmic Anisotropy Polarization MAP-per (CAPMAP) and the Cosmic Background Imager (CBI)-released new measurements of the CMB polarization. The WMAP scientists should also soon release new polarization measurements. In the past few months large new projects, including Q/U Imaging ExperimenT (QUIET) and QUEST at DASI (QuaD), have ramped up their efforts. These and other developments should yield many interesting, and possibly surprising, new insights into the dynamics of the early universe.