CHAPTER FIVE
The standard model of cosmology is so successful that it is now a foundation from which we can look for departures. Through more precise measurements of the CMB we will learn, for example, the total mass of neutrinos. We might find that there are remnant gravitational waves from the birth of the universe that now pervade the universe. We could perhaps find that the cosmological constant isn’t constant or that general relativity needs modification. Perhaps the universe isn’t quite geometrically flat. Perhaps the fluctuations have a slightly different form and spectrum than we now measure. Perhaps a new particle in the early universe will reveal itself. To be able to determine any of these, we need more precise data. Before we touch on five especially active or promising frontier areas—the neutrino mass, gravitational waves, fundamental physics from structure formation, finding clusters of galaxies, and searching for subtle variations in the CMB’s temperature spectrum—we will first introduce a new observational technique: CMB lensing.
The image of the Bullet Cluster (plate 6) shows a clear separation of dark matter from normal matter. The location of the dark matter was found through an analysis of the gravitational lensing of far-distant galaxies by the Bullet Cluster itself. The cluster acts as a lens. We can take this to another level. The Bullet Cluster is a lens not just for the distant galaxies but for everything behind it, including the CMB. If we could measure the CMB with high precision right around the Bullet Cluster, we would see that it is distorted. One advantage of using the CMB as a backlight is that it comes from one surface at a precise distance, so the effect of lensing may be computed accurately. The Bullet Cluster is pretty massive so it stands out, but all the mass concentrations between us and the decoupling surface act as lenses. No matter where we look, the CMB is lensed. The effect is small, but with the current high-sensitivity instruments, it is readily identifiable.
How can we distinguish the underlying CMB anisotropy from the lensed version if it is lensed no matter where we look? The lensing has a distinctive effect on the CMB. It distorts the anisotropy in a special and calculable way. If you viewed the world through slightly textured glass, and you knew the characteristics of the texturing, you could figure out its effects on what you were seeing. In cosmology, the analog of the textured glass is the distribution of matter between us and the decoupling surface, and “the world” is the CMB.
There is a beautiful and deep connection here. Our model posits that the primordial power spectrum gave rise to the CMB anisotropy and to the fluctuations in matter throughout the volume of the observable universe interior to the decoupling surface. If we have the correct picture, we should be able to compute the CMB lensing to high accuracy because we know all the pieces of the puzzle. So far, the lensing of the CMB matches the prediction. This gives us added faith in the standard model because the predictions were made well before the measurements. The lensing measurements have an additional benefit. Similar to the way in which lensing by the Bullet Cluster tells us where the mass is located, lensing of the CMB gives us a two-dimensional projection on the sky of the distribution of dark matter throughout the universe. Maps of the mass distribution are already being made. We expect to continue learning more through CMB lensing in the future. The technique will play a large role in pursuing the first four frontier areas we address now.
Neutrinos. We have already mentioned neutrinos a few times in this text. Until recently they were thought to be massless. We now know they have to be more massive than one ten-millionth the electron’s mass, but less than ten times that. Because there are so many in the universe, about 300 per cubic centimeter, they affect how cosmic structure grows. There are a number of ways they affect the CMB, but one of the most distinctive is through lensing.
If neutrinos are on the light side of the possible mass range, they act somewhat like photons, traversing the universe without affecting the matter distribution. If they are on the heavy side, they still travel quite fast and reduce the degree of clumping in the matter distribution by in effect transferring mass from high-density regions to lower-density regions. The more massive the neutrino, the more the contrast is reduced. The degree of clumping affects the lensing of the CMB because it’s the fluctuations in matter that are producing the lensing; thus the more massive the neutrino, the smaller the lensing signal.
The CMB lensing measurements are not quite sensitive enough to see this effect, but they will be soon. They are also not as informative as a laboratory measurement with regard to the defining characteristics of neutrinos. Primarily what we learn from the CMB is the neutrino’s gravitation effect on the distribution of matter. The CMB observations can’t distinguish between, say, the different neutrino types or other fundamental properties. Still, it would be amazing to determine one of the fundamental properties (the mass) of these most elusive of particles through their gravitational lensing of the CMB. We know so little about them that we might be surprised by what we find.
Earlier we mentioned that neutrinos, as we understand them, couldn’t be the dark matter. We can now see why. If they act the way we think they should, they will stream out of the more dense regions and reduce the formation of cosmic structure. We’d see this in the distribution of galaxies, and we do not. Upcoming surveys of galaxies will be so sensitive that they will be able to see the neutrino’s effects on cosmic structure. There is an opportunity to compare the neutrino’s effect on the CMB and on the distribution of visible light. This is one of the many ways in which the cosmos is becoming a laboratory. There are a myriad of interlocking observations so that the deductions from one individual measurement can be compared against those of another.
In addition to the mass, with the CMB we have already begun to constrain, independently of laboratory measurements, the number of neutrino families. Improved measurements will lead to improved constraints. We might even find that there is a new kind of neutrino, or related particle, that we have not yet seen in nuclear reactions.
Gravitational waves. In many variants of the standard model, a background of gravitational waves is produced in the early universe. They are another form of the quantum fluctuations. In general these waves are a distortion of space and time that propagate across the universe at the speed of light. If a gravitational wave were aimed at a 100 cm by 100 cm plate, then in one half cycle it would shrink the width and expand the height. A half cycle later it would shrink the height and expand the width. If the change in height was 1 cm, we would say the strain is one part in a hundred, or 1%. The Laser Interferometer Gravitational-Wave Observatory (LIGO) detector on Earth detected gravitational waves from a pair of in-spiraling and merging black holes that were about 1.2 billion light-years away. The strain they measured was a part in 1 followed by 21 zeros. This is equivalent to detecting a change in distance between us and Proxima Centauri, the nearest star, which is 4.3 light-years away, with the precision of the width of a human hair. That is a staggeringly precise measurement.
The Big Bang might produce similar waves, in the form of “standing waves,” but with wavelengths ranging in size from about 1% up to 100% the size of the observable universe. Since the wavelengths are so large, the distortions produced by the waves appear stationary to us. Some current models predict the strain should be about a part in 100,000. This is a far greater strain than detected by LIGO. It corresponds to measuring the height of a human to the width of a human hair.
Gravitational waves affect the anisotropy as well as the polarization of the CMB. By stretching and squeezing space, the gravitational waves subtly alter the CMB. The effect is so small that it can’t be distinguished from the anisotropy produced by the primordial power spectrum. However, the gravitational waves affect the CMB polarization in a characteristic way. If we think of the polarization direction as represented by a series of short sticks, primordial gravitational waves impress on them a faint swirly pattern called a “primordial B-mode.” Imagine you threw the contents of a box of round toothpicks on a large black floor so you could see them from the top of a short ladder. You’d want to throw them forcefully enough so that none of the toothpicks overlapped. Let’s say that the orientation of the toothpicks represents the direction of the CMB polarization against the background sky. You then take a picture of it from atop the ladder. The pattern looks random. Now you look at that same pattern of toothpicks in a huge mirror and take a second picture. The last step is to line up the two pictures, the one taken directly of the floor and the one of the mirror image, and subtract them. The part of the first picture that goes away through the subtraction is called an “E-mode” and the part that remains is a “B-mode.” In the standard model, the CMB polarization is almost purely E-mode: it looks the same in the mirror. So far, there are no traces of primordial B-modes.1
A detection of a primordial B-mode would be very exciting. It would provide a new and deep connection between the quantum regime of the very early universe and gravity. It would also provide a new test of fundamental theories of physics when they are extrapolated energies far beyond what can be achieved in an Earth-bound laboratory. If inflation is the correct model of the very early universe, a detection of gravitational waves might be just around the corner. In fact, for the original versions of inflation we should have seen them already. A detection would also have strong implications for cyclic cosmological models. As they are currently understood, cyclic models cannot produce primordial B-modes at a level we might ever hope to measure with the CMB. A detection would rule them out.
To give a sense for how advanced the measurements have become, B-modes have been detected in the CMB. However, they are not from primordial gravitational waves. Rather, they are from the gravitational lensing of the E-modes! The same lensing effect that distorts the anisotropy also alters the CMB polarization. Just as with the lensing effects in the anisotropy, the lensing of the E-modes is at the predicted level, giving us even more confidence that we have the correct model of the universe.
Structure formation and basic physics. It is one thing to specify the contents of the universe. It is quite another to be able to understand how those ingredients combine and work together over billions of years to produce the universe we observe today. By carefully measuring how mass assembles over the ages we can test to see if the cosmological constant is indeed constant with time.
One way to approach the challenge is through a combination of galaxy surveys and the CMB. There are a number of surveys both in space and on the ground that will start to produce massive compendia of galaxies and their characteristics in the next decade or so. The largest on the ground will be the Large Synoptic Survey Telescope. It is expected to measure more than 10 billion galaxies over almost half the sky. Over the same region, deep surveys will be made of the CMB made from the ground. The gravitational lensing signal from both the galaxy surveys and the CMB will be particularly exciting to compare. There are many other ways to combine the data as well. What we expect to emerge is an exquisitely detailed three-dimensional picture of the universe. With detailed interlocking datasets, we can look for tiny departures in the expansion rate versus time from the predictions for an unchanging cosmological constant.
The Sunyaev-Zel’dovich (SZ) effect and clusters of galaxies. The largest gravitationally bound objects in the universe are clusters of galaxies. They are individual identifiable systems made of hundreds to many thousands of galaxies with names like the Virgo Cluster, Coma Cluster, or, as we saw earlier, the Bullet Cluster. A typical cluster is six million light-years across, about 60 times the size of the Milky Way. If towns and villages on a map are like galaxies, clusters are like major cities. One of the characteristics of clusters is they are full of hot gas that is not bound up in stars. This gas emits X-rays, as we saw in the example of the Bullet Cluster.
Rashid Sunyaev and Yacov Zel’dovich pointed out in the 1970s that the hot gas in clusters affects the CMB. The gas is so hot that it is ionized and in essence composed of free protons and electrons. When a CMB photon on its way to us from the decoupling surface interacts with an electron in hot cluster gas, it is scattered. The hot electron gives the photon some of its energy. This alters the spectrum of the CMB shown in figure 2.1, in effect taking energy out of the part with wavelengths longer than one and a half millimeters and putting it at shorter wavelengths. In other words, the scattering distorts the spectrum of the CMB.
This means that if we scan the skies at wavelengths longer than one and a half millimeters, clusters will appear colder than 2.725 K. The dip in temperature is around a thousandth of a kelvin, so with modern detectors it is quite easy to see. More than a thousand clusters have been seen using this characteristic “SZ” signature in the CMB, and before long there will be ten times this many.
One of the features of the SZ signature is that it is almost independent of when the scattering took place. For the same temperature electrons, when the universe was more compact, the CMB was hotter and the corresponding dip in temperature greater. The expansion of the universe cools the scattered photons just as it does with the CMB so the net SZ effect stays the same size. With the SZ effect we can look out to great distances, back to a time when clusters were forming. In a given direction, we can measure all the clusters in the observable universe above some mass limit. We can then see how many there are versus time and compare that to predictions of structure formation. The clusters give us another way to probe the cosmological constant.
Clusters highlight another example of the important link between different types of observations. With the SZ effect, we can’t tell the distance to a cluster or its mass. We need to observe in the visible or infrared to see how far away one is. There are a number of ways to determine a cluster’s mass. Probably the best way is to use gravitational lensing as was done with visible light for the Bullet Cluster. Soon we will have large catalogues of clusters complete with distances and masses and thus another way to look for new elements in the standard model.
The temperature spectrum. We noted earlier that if the source of radiation is a blackbody, all you need to do is specify its temperature and you know the intensity at all wavelengths. To the limits of measurement we know the CMB is a blackbody (away from clusters of galaxies!). Put another way, it is described by the Planck function as shown in figure 2.1. However, if the source is not a blackbody, then the effective temperature depends on the wavelength. This could be the case if there was a large injection of energy during the cosmic evolution, say from the decay of some particle, or if the universe evolved in such a manner that the radiation did not have time to come into equilibrium with the particles. There are a number of known processes that should alter the temperature spectrum at levels a little greater than a factor of ten below current limits. They include the reionization associated with the formation of the first stars and the spectral distortion produced by the SZ effect of the combination of all groups of galaxies and clusters. These signals are too small to detect with the current experimental methods, but instruments are being designed to search for them and other features.
Summary and Conclusions
Let’s take stock of the major themes we’ve discussed. In chapter 1 we got a sense of the almost overwhelming vastness of the universe. The Milky Way is just a speck of dust in the cosmic expanse. And recall, it contains 100 billion stars and most of those have planets. From a cosmic point of view, Earth is insignificant. A starting point for making quantitative sense of the vastness is Einstein’s Cosmological Principle. When the principle is meshed with observations, we find that if the universe is averaged over 25 million-light-year-diameter spheres, it more or less looks the same no matter where we are. In other words, from a coarse-grained perspective, the universe is homogeneous.
We also saw that this whole vast landscape is expanding. What’s more, the expansion is accelerating. Again, these are observations, not theories. This is the way the universe acts. One way to think about the observations is that space itself is expanding and that the contents are going along for the ride. But we don’t know why space would expand. It is just a description. By extrapolating the expansion back in time, we realized that there was a beginning a finite time ago, in fact 13.8 billion years ago. It may not have been the beginning for all existence and for all time, but it was the start for our observable universe. Knowing that the speed of light is fixed made us realize that the farther out in space we peer, the farther back in time we look: remember, telescopes are like time machines. When we look back far enough, we see the CMB.
In chapter 2 we took a tally of the major constituents: the CMB, the atoms, the dark matter, and the cosmological constant. We know there have to be more components—for example there should be neutrinos—but they are subdominant enough that the model doesn’t need them to account for the observations. The atoms are conspicuously clumped into galaxies; these are our cosmic signposts. The dark matter distribution is more puffy than that of the atoms, but it is still clumped. The energy density associated with the cosmological constant suffuses space. As far as we have been able to measure, it is not clumped. The CMB also suffuses space, but its energy density is insignificant compared to that of the atoms, dark matter, and cosmological constant.
After describing, in chapter 3, how we measure the CMB and reduce the anisotropy maps to a usable form, we turned to the interpretation of the data in chapter 4. Going back to the beginning of the book, perhaps the most amazing thing about the universe is that we can understand it at its grandest scales to percent-level precision. In a nutshell, a hot, dense universe expanded from a fiery beginning that we call the Big Bang. Quantum fluctuations intrinsic to the fabric of the primordial spacetime, and expanded by the rapid early expansion, grew into fluctuations in the strength of gravity throughout space. The CMB gives us a two-dimensional snapshot of these fluctuations some 400,000 years after the Big Bang. As the universe evolved, the dark matter and atoms responded to the variations in gravity to eventually form all the structure in the universe. The cosmological constant, initially inconsequential, now drives an accelerated expansion and will increasingly dominate the universe.
It is remarkable that humankind has arrived at the standard model of cosmology. We cosmologists feel fortunate to have been alive in the decades when the explosion of knowledge about the universe took place. Most of us in the field recall a time when we did not know the geometry of the universe, its contents, or its age. As the data have become more and more precise, whole classes of cosmological models have been shown to be wrong. As we have emphasized, it is precise measurements that are the foundation of the standard model. The dramatic advance in cosmology has occurred through the ability to compare models to measurements. It turns out that the early universe is simple and that the physics that describes it is straightforward. It did not have to be this way, but Nature was kind in letting us learn so much.
We now have a powerful and predictive model, but even within that context there are still many open questions. Some we can address with better measurements or deeper theories: What is the dark matter? Why is it that our universe is predominantly matter as opposed to a combination of matter and anti-matter? What is the physics of the very earliest times? What is the cosmological constant telling us about the vacuum? As far as we know there is no particular “need” for it. Although we talk about “expanding space,” we do not really know what space is. The clues may well be all around us but we haven’t thought of them in the right way. There are questions we may never be able to answer conclusively: Are there multiple universes? Are we in just one of an endless series of cycles?
The cosmos has captured the imagination of humans since time immemorial. Although the recent advances are dramatic, the quest for ever deeper knowledge on both theoretical and experimental fronts continues. For those observing the cosmos, nothing is more exciting than finding something new, or learning that one of the elements of the standard model needs to be considered in a new light. There is a huge amount left to be learned from the CMB, and we will likely be measuring it for years to come.
1 Primordial gravitational waves produce E-modes and B-modes equally, but the E-modes are not as readily distinguished from the rest of the CMB as the B-modes.