Fear of a Black Universe

by Stephon Alexander

  7

  WHAT BANGED?

  The universe is expanding. Why should we care? After all, it seems like the expansion has no effect on us, right? We are bound by gravity to our solar system, and if you look out at the night sky, you see stars, no different from our own sun. Like grains of sand on a beach, our sun is as typical as the other stars in our galaxy, filled with hundreds of billions of suns. But the expansion of the universe matters to those stars, which means it matters to us. Stars are necessary not only for sustaining life as we know it with their light and heat, but for functioning as the manufacturer of the material of planets and life. As we will soon see, there is a startling connection between the early evolution of the universe and the creation of the substances necessary to form stars, which points to a delicate interplay between gravity and quantum physics. And some of this interplay remains unsolved.

  Einstein taught us that space and time are more than the location of an event, but that, like electromagnetism, space-time itself is a dynamical—in its case, gravitational—field. Not only does matter live on space-time, but space-time lives on matter. Our most direct experience of this fact is that the sun warps the gravitational field, like a sitting person’s weight warps a cushion, bending space-time and creating orbital contours through which planets can move. In general relativity the space-time field, called the metric tensor, encodes information about the curvature of space-time in the presence of matter and energy. As John Wheeler famously states, “Matter tells spacetime how to bend and spacetime tells matter how to move.” But space-time can dance in many different ways depending on the configuration of matter and energy that interact with the gravitational field. A famous example is the spherically symmetric space-time of a black hole that is sourced by a collapsed star. The mass density is so high that space warps such that the emitted light cannot escape the highly curved space-time.

  By now it is popular knowledge that the universe is expanding, and this has been experimentally confirmed by looking at receding galaxies and racing away exploding stars called supernovae. When the distribution of matter and energy is the same in every direction and at every point in the universe, the equations of general relativity predict that the universe’s space-time will expand. A simple way to intuit this type of physics is to imagine the surface of an expanding balloon with points fixed on the surface. Imagine that all points on the balloon’s surface is the environment of a galaxy.

  As the balloon expands, the galaxies appear to recede from each other. An observer in a given galaxy is fixed at the same point on the balloon’s surface despite its expansion. What’s moving is the space (rubber) between the points, or galaxies, on the balloon. If you can imagine that a region on the surface of the balloon is a region of three-dimensional space, then the analogy comes pretty close to illustrating the dynamics of an expanding universe. Where does the analogy break down? The rubber makes up the balloon, but space in our universe seems empty, yet dynamical. It appears that space is continually being created in an expanding universe, and we will discuss this perplexing fact in a later chapter.

  But what is the significance of the expanding universe, aside from making our universe extremely large to house billions of galaxies? Even after I wrote my first research paper that involved some new features of the expanding universe, I wondered about that question, but was too embarrassed to mention my puzzlement to others. I soon discovered that a copioneer of the expanding solution of general relativity was a Belgian Catholic priest and theoretical physicist, Georges Lemaître, in 1927, who was driven to reconcile his religious beliefs with his love of and conviction for the veracity of general relativity.1 From this solution Lemaître predicted that the expansion would make galaxies recede from each other at a speed that is proportional to the distance between them. Two years later Edwin Hubble confirmed this prediction by showing with telescopic data that the light emitted from galaxies was redshifted as predicted by Lemaître’s expanding solution—indicating that galaxies are moving away from each other and us.

  Lemaître seemed to have been able to reconcile his religious conviction with the materialist explanation from relativity theory by positing that the universe emerged from an initial point of “creation” where all the matter in the universe was concentrated. He called this point the “primeval atom” or the “cosmic egg, exploding from the moment of creation.” This view of the creation of the universe is also found in many proto-Indo-European and African cultures. This later became known as the big bang, coined by English astronomer Fred Hoyle, who was a proponent of a competing theory coined the steady-state universe. Lemaître says it quite poetically: “We can compare space-time to an open conic cup.… The bottom of the cup is the origin of atomic disintegration; it is the first instant at the bottom of space-time, the now which has no yesterday because, yesterday, there has no space.”

  According to Lemaître’s solution, distances increase as time in the universe elapses. If we run the cosmic clock backward then there will be a time in the past when all distances tend to zero, leading to the nonexistence of space. The geometry of this expanding universe can be recast in a mathematic form that the universe’s beginning looks like a point in a four-dimensional surface that spreads into a cone in the future. The priest intuited that the entire content of the universe was contained at this point of origin, the “bottom of the cup” that he called the “primeval atom” that burst into an expanding cone. However, he did not provide a mechanism for this disintegration of the primeval atom, nor what conditions led to this initial state of the universe. And there is another serious problem associated with this state of infinite density. As the universe shrinks, the curvature tends to infinity. When physical quantities of a theory go to infinity, we call it a singularity and it usually means that the theory itself breaks down and can’t be trusted. But there are some subtleties about cosmic singularities that deserve more attention and background, which we will discuss in a later chapter. History has shown that singularities signal new physics that may resolve the singularity. But there is another clue that may give us insight about the very birth of our universe’s space-time and what may have sourced it.

  When the expanding universe was smaller and denser, it was much hotter. Starting from the big bang as the universe expanded, roughly one hundred thousand years later the temperature cooled such that its energy was enough for electrons and protons to bind, forming hydrogen. During that moment the last photons would be liberated into space, leaving a thermal afterglow at the energy associated with the binding energy of hydrogen. This is the last fossil light of the early universe that would persist to propagate throughout the universe with a temperature of three thousand degrees Kelvin. But as the universe expanded by a factor of one thousand since the CMB epoch, we should expect to find this light radiation in every direction at this temperature. Physicists were on the hunt to find this afterglow, which was coined the cosmic microwave background radiation (CMB). Finding it would be a smoking gun confirmation of the expanding universe. The Nobel Prize–winning discovery was made in 1967 by Arno Penzias and Robert Woodrow Wilson, two Bell Lab scientists who first thought that the signal was a contamination from pigeon dung. Down the street at Princeton, physicists such as Robert Dicke and James Peebles were looking for the afterglow radiation from the big bang, but with no success.

  FIGURE 11: This is a Penrose space-time diagram of an expanding universe (top) and a collapsing one. The jagged lines represent the big bang (crunch) singularity, and the solid diagonal lines represent the horizon.

  When we look in opposite directions in the night sky, we see that the CMB photons each took 13.8 billion years to travel to us. Those antipodal photons would take over twenty-six billion years to reach each other. Because the photons travel at the maximum allowed speed, we can know the largest distance possible the photons could have covered, the horizon. Since those photons all existed at the time the CMB existed, we can ask if they had enough time to speak to each other at some earlier time.
The time between the big bang and when the CMB existed is three hundred thousand years; we find that the photons were never able to be in contact with each other. In other words, they are outside each other’s causal horizon. How is it that the photons that cannot communicate with each other attain the same temperature? Some unknown physics that seems to break the speed-of-light barrier between the big bang and the CMB, which is about one second in the expansion history, had to take place so that the photons had the same properties. Otherwise, there is a bizarre coincidence that gives these photons the same properties that appear to occur faster than the speed of light. However, this would violate Einstein’s principle of special relativity—the speed of light is finite and universal.

  But it’s not only the CMB photons that seem to have a nonlocal origin. After all, if the universe were completely filled with only photons and electrons, it would be a boring place. How did all the stars, galaxies, and clusters of galaxies come about? In 1989 a more precise measurement of the CMB was made and tiny ripples in photons were found. An analysis of the distribution of these ripples showed that they matched the superstructure of galaxies in the universe today—those tiny ripples eventually grew into the stars and galaxies that occupy our current universe. Here is how it happens.

  FIGURE 12: A light cone connecting Earth (at top of image) to the big bang (at bottom). Three other light cones specify the histories of three causally unrelated events in the universe’s past.

  The physics of the CMB plasma is like a seething hot ocean of a fluid that’s made up of electrons and photons. This cosmic ocean is dancing with waves that have a special pattern called scale invariance. This scale-invariant pattern has a property that the size of waves of all different frequencies is the same—like zooming in on the plasma and seeing the amplitude of smaller waves look the same as larger ones. A random chaotic fluid does not have this pattern, and some special conditions need to set up an undulating plasma with this type of scale-invariant pattern of waves. But what is the purpose of these scale-independent waves? Let’s focus on one such wave.

  Plasma waves are nothing but pressure waves and are plentiful in nature. Familiar sound waves in the hollow column of a flute is a pressure wave. When a pressure wave is at its peak the mass density and pressure of the wave is maximized. In a gravitating medium like space, these regions of high density will gravitate more than regions of lower density. While these waves in the CMB are oscillating from regions of high to low pressure, space is expanding and cooling the average temperature of the plasma. Eventually the electrons get captured to form hydrogen atoms and get gravitationally attracted to the waves of high density. The hydrogen atoms start to cluster together and become candidates to form the first stars. The equations that govern the oscillations and infall of the hydrogen are given by considering a special form of general relativity called the perturbed Einstein equations. Within a few months of me writing this, my colleague Jim Peebles won the Nobel Prize in physics for solving these equations and illuminating the correct physics that led to the formation of the first structures in the universe from this nearly scale-invariant spectrum of the CMB’s waves.

  FIGURE 13: To the left, during the recombination, epoch electrons and photons exist in thermal equilibrium. They have the “fluidlike” properties of a hot plasma. To the right, after recombination, the universe cools and electrons become bound to the protons, forming hydrogen, liberating the CMB photons.

  The details of how this happens make a more complicated, but straightforward story. It turns out for Peebles’s equations to correctly describe large-scale structure of the universe, the CMB also will have to have extra gravitational pull from overdensities of a new component of matter, namely dark matter.

  Unlike the plasma waves, dark matter is required to have zero pressure. If this dark matter overdensity has no pressure, then its oscillation will come to a halt almost immediately. This is because pressure waves, like springs, resist compression and push back against compression with more force the more they are compressed. These two opposed forces of compression and resistance create periodic oscillations. On the other hand, when the dark matter settles down into various regions in the sky, the nearby hydrogen will experience even more attraction toward the dark matter overdensity, enhancing its tendency to form structures, such as stars and protogalaxies.

  There’s a major problem with this picture, however. The space-time structure of the expanding big bang universe does not allow enough time to generate the pattern of scale-invariant waves. So, something special had to happen before the CMB epoch that set up all these waves, like a cosmic conductor telling all waves to oscillate at the same time and loudness. For that to be true, the expanding universe and the observed properties of the CMB—it even seems as if our existence—arise from a mysterious nonlocal phenomenon in the early universe, what Einstein called spooky action at a distance. Physics acting beyond the horizon and sensitive to a big bang singularity seems like an inevitable affair to explain our current existence, and this will require us to consider the possibility of nature exploiting some quantum magic.

  The magic of dark matter isn’t just that it provides the missing gravity necessary to hold the universe we see together. Many of us take for granted that next year will come, because we assume that our solar system’s orbit is stable—without dark matter it is not.

  8

  A DARK CONDUCTOR OF QUANTUM GALAXIES

  The energy in the undulations that grew under gravitational collapse some fourteen billion years ago needed an invisible form of matter to efficiently form the billions of galaxies including our own Milky Way.

  We can measure the effects of dark matter in different ways. The rotation of stars in galaxies is the most direct. Today we see the striking presence of dark matter in all galaxies, which is inferred from an anomalous rotation.1 How is this? When we look at gravity at distances comparable to our galaxy, it fails to account for the motion of our sun and solar system around the Milky Way. The speed of a star like our sun around our galaxy is proportional to the amount of mass it contains. From this, we can infer from the sun’s velocity that about 85 percent of the mass is missing or invisible/dark. In other words, our sun is moving so fast that if there weren’t some hidden form of matter providing the necessary gravitational pull, it would fling off from the Milky Way into oblivion. We have even found that every galaxy is made up mostly of dark matter.

  A second way we can measure the effects of dark matter is through a phenomenon called gravitational lensing. Similar to the bent lens of a magnifying glass, a gravitational lens is a region of warped space that causes light that traverses it to get distorted. Imagine that there is a massive blob of dark matter in front of a galaxy. Although we will be able to see a visible galaxy that lurks behind the dark blob, the image of the visible galaxy will appear to be distorted in a definite way according to general relativity. We can infer the mass of the dark blob from the lensed image of the visible galaxy.

  So, we now know from observations that dark matter exists in individual rotating galaxies and clusters of galaxies that form a cosmic web of interconnected galaxies spanning cosmic distances. I fooled a neuroscientist who thought that a picture of this structure looked like how the brain is wired with neurons. There is invisible dark stuff that pervades the universe, and aside from being the cosmic glue that keeps stars like our sun in orbit, invisible things have a way of being taken for granted. So why are physicists and astronomers so interested in dark matter? We believe that unveiling dark matter is a puzzle piece that will help us understand the fundamental nature of our physical world. And we suspect that once we crack the dark matter code, we will come to know something unanticipated. After all, did Einstein ever imagine that the quantum nature of the photon would lead to solar cells? Ever since its discovery, we have been cooking up theories to account for dark matter, and despite our efforts, we have not been able to identify the one true model behind its mystery. We are not short of imagination, as there are hun
dreds of candidates for the identity of dark matter. Let’s say that you wanted to construct your dark matter model. There are some necessary criteria that it needs to satisfy.

  Our standard big bang cosmology suggests that dark matter may have been born in the very early universe at least fourteen billion years ago along with the visible matter, and based on the observation of the cosmic microwave background radiation, both dark and visible matter were distributed across the universe soon after their creation. After the dark matter is created, it must remain stable throughout cosmic history, meaning that it cannot annihilate or decay so that it can cluster to form the scaffolding for the visible matter to form stars and galaxies. Second, for the dark matter to do its job to aid gravity in sculpting the cosmic structure, it must be cold, or equivalently, the dark particles must be motionless, which endows dark matter with the properties of a pressureless, frictionless fluid. The opposite of this is a gas of particles bouncing around so fast that their high momentum would make them hot, which would not allow structure to form.