Fear of a Black Universe

by Stephon Alexander

  To date, the most accepted and experimentally compelling paradigm of the early universe is cosmic inflation. The critical message of inflation is that every bit of structure in the universe, including planets and living things, emerged from quantum fluctuations from a vacuum state that contains the inflaton field’s potential energy—the inflaton is called that because it drives inflation—and nothing else. Nevertheless, what physicists call virtual particles can emerge spontaneously from the vacuum, and these are important to explaining how both matter and large-scale cosmic structure emerged from nothing. And although there are alternatives to cosmic inflation, such as the big bounce and cyclic cosmologies, which attempt to alleviate the problems that plague inflation (we will discuss some of these alternatives in the next chapter), none of them are free from the influence of virtual particles. No matter which way we slice it or which model we prefer, the idea that all matter and structure in the universe came from virtual quantum processes is inescapable, counterintuitive, and requires a more in-depth examination. After all, nature has to figure out how to make virtual particles real particles. And indeed cosmic inflation has a clever trick up its sleeve to make this happen.

  In quantum field theory, virtual processes are ubiquitous and have been measured in the lab. A consequence of these virtual processes are virtual particles, which are particles that quickly materialize and disappear into the vacuum before having any material consequences. The vacuum is not empty but seething with rapid interactions of quantum fields and particles. Remember that quantum fields comprise oscillator modes that vibrate in the vacuum state. These field oscillators also interact with other field modes. A virtual process occurs when field modes spontaneously activate to create a particle, and like a fish leaping out of the sea the virtual particle quickly returns back to the vacuum state. An example of this is when an electron and positron get pair produced from field oscillations and almost immediately annihilate into the vacuum state. Therefore under normal circumstances, these virtual particles never materialize into real ones.

  It is the uncertainty principle that is at the heart of virtual processes, and it is remarkably dictated by the following relation, which says that the uncertainty in the energy of a virtual process is inversely proportional to the uncertainty in time that the process occurs. According to the uncertainty principle, extremely microscopic time scales correspond to very high energies, enough to pair produce matter and antimatter from the vacuum state. For all practical purposes, the vacuum is continually creating and destroying particles at a rate so fast that we do not “see” them because they are too short-lived.

  Using Einstein’s relation that equates energy with mass, we can find the condition to create two particles of a given mass out of a field that carries the necessary amount of energy. As an example, if we combine Einstein’s energy-mass relation, stated above, along with the uncertainty principle, we find that it is possible to create electrons and positrons during a time interval that is roughly a trillionth of a trillionth of a second! During that time the particle and antiparticle pop into and out of existence (because they soon annihilate). That’s why we never see virtual processes in everyday situations. As we will now see, according to inflationary theory, all the matter that exists around us, including ourselves, were originally virtual particles. How is this possible?

  In everyday situations where the curvature of space-time is nearly flat, virtual quantum fluctuations are incredibly short-lived and remain quantum—they never take on all the characteristics of a classical particle. But inflation produces these virtual particles, and somehow they do become classical. Recall that in quantum mechanics, the collapse of the wave function requires a mechanism to solve the measurement problem. The Copenhagen interpretation postulates that a classical measuring device or observer collapses the wave function. However, there are no known observers or classical apparatus during or soon after inflation that we can postulate to collapse the wave function of these virtual states. Therefore, inflation has a cosmological measurement problem.

  FIGURE 17: A Feynman diagram of a virtual process. The wavy line represents an incoming photon, which emits a virtual particle, represented by the closed loop.

  However, due to the dynamic nature of the expanding space-time during inflation, virtual processes play a central role in becoming the very seeds of structure in the universe. Let’s take a deeper dive into the virtual processes during inflation. One interesting phenomenon is the exponential expansion of space-time feedback into the dynamics of the quantum vacuum fluctuations, causing them to reduce their uncertainty. The reduction in uncertainty transmutes the oscillations to be a coherent state. This might sound fanciful, but in fact, these states are identical to when photons collectively become a coherent laser beam. These coherent states undergo a phenomenon called quantum decoherence, which washes out all the quantum phases in the wave function, rendering the primordial quantum fluctuations into classical seeds for cosmic structure. The key to virtual processes during inflation is that the time during which inflation happens is shorter than the time scale, dictated by the uncertainty principle, necessary to produce the observed particles around us. Inflation can last as quick as a millionth of a billionth of a billionth of a second. During this short time, the inflaton dumps its potential energy into the production of virtual quantum particles. These virtual particles live long enough and simultaneously get stretched to transition from virtual particles to real classical particles such as electrons, quarks, photons, and others produced in the big bang.

  FIGURE 18: Schematic representation of inflation in the universe.

  Cosmic inflation was invented by my mentor Alan Guth to solve a handful of problems that plagued the standard hot big bang paradigm, especially the horizon problem that we discussed earlier. Inflation’s magic stems from a short burst of exponential expansion of the universe, transforming a microscopic universe into the macroscopic one we inhabit. Soon after, the inflationary theory was improved by Andrei Linde, Andy Albrecht, and Paul Steinhardt to address some technical problems in Guth’s original proposal. The potential energy for inflation is ignited during the Planck epoch, which is the earliest stage of the big bang, during which quantum effects are expected to reign supreme due to the universe’s microscopic size and high energy scales. A large amount of potential energy can transform into kinetic energy of the gravitational field, creating an exponentially fast expansion rate. The consensus from theorists is that this energy is contained in a new spin-zero quantum field called the inflaton. On the largest scales, this field has to be smooth and homogenous to create the observed homogeneity seen in the night sky: like a well-shaken bottle of milk, the sky looks pretty much the same whichever direction you choose to look. During the rapid expansion, a few magical things simultaneously happen. First, all present quantum field oscillations get created from the vacuum and stretched by the expansion. This happens because the part of the gravitational field that expands, known as the scale factor, directly couples to the wavelengths of quantum vibrations, acting like a volume amplifier in a cosmic stereo. As the scale factor increases, wavelengths likewise get stretched.

  This basic picture of cosmic inflation is compelling and makes the correct prediction of the observed properties that we measure in the fluctuations of the cosmic microwave background radiation. Indeed, the so-called empty space in the early universe, if it is dominated with vacuum energy, comes alive through the engine of inflation, to convert this potential energy into the observed particles and radiation we see. The magic behind inflation is its effect on general relativity to create an exponential expansion of space itself. All that existed in this infant universe were quantum fluctuations riding along with this inflationary era. And it is their particle excitations that get created out of the vacuum of space-time that becomes all the observed matter around us, including us. However, there remain some foundational problems of inflation that need to be addressed.

  FIGURE 19: The wiggly lines represent the quantum den
sity fluctuations sourced by the epoch of cosmic inflation. At later times these density fluctuations grew, with the help of dark matter, to form galaxies.

  The quantum birth of matter and antimatter during inflation is a very promising avenue for generating the observed asymmetry between matter and antimatter that characterizes our universe today—that is, for solving the problem of baryogenesis. Inflation does the job of producing matter, but it also produces antimatter. Unless matter over antimatter can be produced either during inflation or after, we are left with a world of equal matter and antimatter, and that’s not our world. If there were a way to bias the production of matter, then we would explain a big part of why we don’t see galaxies, planets, and stars made of antimatter. There have been heroic attempts to account for baryogenesis in the early universe, and most models assumed that the necessary ingredients occurred after inflation, and this made good sense. The rapid expansion of inflation expands the volume of space so much that an initially large number of particles would dilute away. But aside from this issue, two conditions spelled out by Sakharov are naturally satisfied during inflation—particle production and the out-of-equilibrium condition.

  The key lesson behind inflation is that our classical world of galaxies, stars, and planets emerged from a quantum origin. However, the baryon asymmetry was established either during inflation or by new physics after inflation. In 2004 my collaborators Michael Peskin and Mohammed Sheikh-Jabbari and I developed a theory that shows how inflation can solve the problem of baryogenesis. And this idea, many years later, also provided a way to generate a specific breed of dark matter. The key to this mechanism is to realize that the very agent that ignites inflation, the inflaton field, can interact or couple with matter and antimatter in an asymmetric manner that violates CP and baryon number in one fell swoop. This is elegant because instead of struggling to satisfy the three Sakharov conditions independently, the inflaton meets them all in one shot.

  That doesn’t solve all the challenges facing inflation, however. Inflation assumes that quantum fields, including the inflaton field itself, are subject both to the laws of quantum mechanics and to gravity. Gravity is mostly classical. However, for inflation to do its magic, some aspects of gravity have to be quantum mechanical as well. The seeds of structure, including the virtual processes, are genuinely born when they interact with quantum undulations of the gravitational field. These undulations are small compared to the part of the gravitational field that undergoes homogeneous growth in three spatial dimensions. But we are free to ask, why not quantize all gravity? Nothing stops the tiny quantum fluctuations of the gravitational field from growing the closer we get to the time that inflation begins. Why should we fully quantize the matter fields and not fully quantize gravity?

  The quantum fluctuations of inflation also involve quantum fluctuations of the gravitational field. And as we go back to earlier times when inflation itself was ignited, these quantum gravitational fluctuations approach a big bang singularity hinting at a need for a full treatment of quantum mechanics and gravity, a theory of quantum gravity. We will see that quantum gravity and inflation forces some sharp questions about assumptions we make about physical reality. But to get to the question of gravity, let’s consider something like antigravity first.

  10

  EMBRACING INSTABILITIES

  A global virus pandemic brings the world to its knees. The stock market suddenly drops, inciting fear from investors. A star collapses to form a black hole. These events all have one thing in common. They are all instabilities that correspond to a catastrophic growth in some quantity that leads to an unwanted outcome. In physics, sometimes the bad outcome of an instability threatens to obliterate the validity of the theory itself. The quantum revolution was born in part as a result of taming instabilities in atomic systems, such as the ultraviolet catastrophe and the instability of classical atomic orbits. In recent times, billion-dollar particle accelerators were built to look for supersymmetric particles that function to tame an instability that would lead to a catastrophic growth in the masses of all matter. No diet would help us for such an instability. Many physicists were confident that this pattern of fixing instabilities would lead to experimental confirmation of supersymmetry, but it didn’t happen. Are all instabilities tragic, or are some useful for our universe’s functioning in hidden ways that could lead to new directions in our understanding? What are instabilities, especially of the quantum type, trying to tell us about the new physics?

  My colleague João Magueijo at Imperial College developed a theory of the early universe that solved the infamous horizon problem and flatness problem in cosmology. In ordinary relativistic cosmology, the horizon problem describes the fact that the edges of the universe seem to have been in communication with each other, despite being too far apart for light to have traveled from one far-flung region to another in the time the universe has existed. The flatness problem has to do with why there’s just the right amount of energy in the universe so that its geometry is Euclidean and flat. In Magueijo’s theory, he posited that in the earliest stages of the universe, the speed of light could vary in time, at odds with Einstein’s postulate of the constancy of light. Magueijo presented a mathematical model of his theory in a publication that was later contested by some theorists as being a sick theory, because it seemed to give rise to instabilities if the theory were to be quantized—to some aficionados, it was not even wrong. I was there for the showdown, and Magueijo, being a black belt, enjoys these physics sparring sessions. We were sitting at a seminar and the invited speaker made reference to Magueijo’s theory and claimed that it was sick because it had an instability. Magueijo responded, “I want the damn instability. After all you are an instability!”

  What Magueijo meant was that the chain of cosmic events leading to life were ignited by instabilities. These tiny perturbations in the CMB that grew to form the first structures is an instability in the equations that govern those cosmic structures. These good instabilities get regulated and stabilized when the system becomes nonlinear and highly interdependent with the gravitating environment. Today physicists are wrestling with strange instabilities that continue to cause the physics community headaches. We will place our focus on an instability that is found in empty space, a vacuum instability that communicates with everything otherwise known as the cosmological constant or dark energy problem.

  Recall that the discovery of quantum mechanics was ignited by a handful of instabilities found in classical physics. Our very existence owes to the stability of the atomic structure of hydrogen and oxygen in water molecules, but classical physics predicts that all electrons should spiral into protons, making the classical atom unstable. Every time the electron orbits around the proton it radiates away electromagnetic energy, which reduces its distance to the proton. Eventually it spirals into the proton, rendering the atomic system unstable. By quantizing the orbits of the electron by associating each orbital distance with a wave, the electron, like the lowest vibration on a guitar string, would have a lowest orbit allowed.

  Another type of instability is when a system’s energy continues to grow without bound. This is similar to falling down an infinite hill—your kinetic energy would continue to increase until it reaches infinity. And this contradicts relativity, which says nothing can go faster than light. Ironically, while quantum mechanics was invented to tame classical instabilities, it was later discovered that even quantum systems can have instabilities. For instance, when we consider the quantum effects of electrons, what we perceive as empty space in front of us turns out to contain a form of energy due to the activity vibrating quantum fields. This contribution to energy (often called vacuum energy) is very large and should dominate the energy of the universe, causing this expansion to accelerate so fast that galaxies would not have a chance to form. This is known as the cosmological constant or dark energy problem, and as of today there remains no solution. Let’s understand this at a deeper level.

  As we explored previously,
the fundamental substance behind all matter and force carriers known to us are quantum fields, and they all generate vacuum energy. As we saw earlier, one consequence of quantum fields is that empty space is not empty; it is filled with vibrations of quantum fields that, in the universe’s past, built all substance from stars and planets to life itself. Thus, empty space is occupied with these vibrating, interacting quantum fields. Recall that a quantum field has properties like a large collection of oscillators. Because of the uncertainty principle, a quantum field oscillator can never be at rest.1 For such a system the rate of vibration is proportional to the field’s energy and can emerge as a particle from empty space like a water droplet that jumps on the surface of the ocean.