Fear of a Black Universe

by Stephon Alexander

  The baryogenesis problem makes clear that just as every particle is created, so too is its antiparticle created, but only for a short moment of time, beyond our ability to see with our naked eyes or our most advanced high-speed shutter cameras. This spontaneously created pair of particle and antiparticle quickly meet and annihilate each other, back into empty space. What’s the use of that? This process is called a vacuum bubble, and it generates energy. Gravity likes energy. There are other similar effects that likewise generate vacuum energy. In every chunk of empty space, the vacuum energy can be envisaged as completely transparent quantum fluid that differs from ordinary fluid. If you try to compress an ordinary fluid like water, it will resist compression and push back on you; this is positive pressure. The vacuum fluid has negative pressure and does the opposite. Try to compress it, and it will expand outward. The effects of quantum vacuum energy in empty space have been confirmed in the lab and they are tiny. But the predictions of our standard model predict a much larger amount of vacuum energy. And all forms of energy according to general relativity, including vacuum energy, will warp space-time. So, how exactly does vacuum energy affect curved space-time?

  If there is one key lesson to take away from Einstein’s theory of general relativity it is that space-time is also a field. The matter fields and their vacuum energy are tethered to the gravitational field, causing it to warp. The vacuums’ negative pressure stretches space by accelerating observers away from each other, resulting in a repulsive force. For instance, if there was a lot of vacuum energy near the earth and the moon, space would stretch rapidly outward and they would fly away from each other. Now comes the punch line. In 1998, groups led by astronomers Saul Perlmutter, Adam Riess, and Brian Schmidt observed with powerful telescopes how distant, exploding stars recede away, and showed that the expansion of the universe is accelerating. The only way this can happen is if the universe were filled with vacuum energy. But there is a major problem: according to precision calculations in quantum field theory and general relativity, the expected and observed vacuum is 120 orders of magnitude smaller than what our standard model predicts. You may wonder why there is all the fuss about this discrepancy between our most precise theoretical characterization of modern physics and our observations. For one, it says that something is wrong with either general relativity or quantum field theory, or both, in describing the quantum effects of fields on space-time. Alternatively, there is some unknown reason why the vacuum energy is either hiding itself or tamed by some new, mysterious, unknown physical force—yet to be discovered.

  FIGURE 20: Systems can be stable if the potential energy is bounded from below, as seen to the left. The middle metastable graph shows a bounded potential locally, but unbounded to the left. So, this particle can be both stable and unstable depending on its energetics. An unstable system has a potential that is unbounded in all directions.

  The form of vacuum energy that generates the universe’s acceleration is popularly known as dark energy. Our understanding of precision physics predicts an instability in the production of dark energy. In other words, there should be too much dark energy and the universe should have accelerated much too fast earlier on to even form stars, galaxies, and us.

  After a research stint in London, I headed out to the hills of Silicon Valley to continue my research at the Stanford Linear Accelerator Center (SLAC), known as one of the meccas of particle physics. My new colleagues at SLAC and Stanford were some of the pioneers in string theory, a theory that realizes Einstein’s dream to unify all four forces. The idea of string theory is simple and elegant; the articulation of the theory requires some of the most advanced mathematics known to us. My new colleagues had worked for decades along with a global community of string theorists to develop this elegant ten-dimensional, yet abstract framework. Young physicists like myself were handed the baton in this quest. String theory provided a rich framework to address problems that share residence in particle physics and cosmology. This is mainly because string theory naturally links the extra dimensions with gravity and hidden symmetry patterns found in the standard model of particle physics.

  There are strong reasons to believe that string theory could very well be the theory that underlies our reality. As we will explore in an upcoming chapter, string theory unites quantum mechanics with general relativity by taming disastrous ultraviolet (short wavelength) quantum instabilities.2

  Once cosmologists measured the amount of dark energy (also known as vacuum energy or the cosmological constant) deduced from the acceleration of space-time, we had to reckon this fact with our precision theories. We know that the standard quantum field theory interacting with general relativity was not enough. This was an opportunity for more fundamental theories such as string theory, which had ingredients of taming certain short scale instabilities, to come to the rescue. We saw this as some experimental guidance for our theories, places where the theories could possibly make contact with the real world and tell us why the universe was accelerating at this epoch in cosmic history. However, a major set of challenges presented itself. String theory is blessed with symmetries that tame infinities, but the symmetries themselves did not straightforwardly allow for a positive cosmological constant, let alone the tiny value that exists in our universe. I approached the head of our group and asked him for some guidance in how I and the other postdocs might navigate through the difficulties and confusion. His advice was to find an example of a solution from string theory that admits any positive cosmological constant. We were all on a hunt to find this solution. Within a year my colleagues Shamit Kachru, Renata Kallosh, Andrei Linde, and Sandip Trivedi found a remarkable pathway and solution of realizing a cosmological constant in string theory. And this had to do with finding a special space-time solution in string theory called de Sitter space.

  Solutions of general relativity that admit a positive cosmological constant were known since the inception of the theory. One solution was discovered by Willem de Sitter, and as expected, it gave accelerating space-times; the larger the cosmological constant, the more the space accelerates, and by an exponential amount. During the early stages of the universe’s expansion, there was a fine balance between the repulsive expansion of space and the attractive gravitational pull of infalling matter to form the first stars and galaxies. The Nobel laureate Steven Weinberg realized that if there was too much vacuum energy in the universe, the repulsive force would overshadow the attraction necessary to form structures and there would not be any structure, hence there would be no life in the universe; there would be no universe as we know it. The universe seems to have dialed in just the right amount of vacuum energy for structures and life as we know it to exist. So it is up to our theories to understand not only why vacuum energy is positive but also why the exact amount needed for the existence of the universe is observed—we call this the “why now?” or coincidence problem. Unfortunately, as we’ve seen, our current understanding of physics produces far too much vacuum energy. So, the real question is: What happened to all the vacuum energy that we expect to exist? Or let us assume that all this vacuum energy does exist, so then why does gravity not respond to vacuum energy? This remains a mystery.

  During my time at Stanford, young string theorists like me were seeking out pathways in the jungle of ten-dimensional calculations to find solutions that have a small and positive cosmological constant. Then, in a groundbreaking paper, renowned theorists and friends Raphael Bousso and Joe Polchinski argued that the search to find such solutions could be futile. I’ll come back to their work later in the book; for now it’s enough to say that it essentially argued that the universe was just one of many, which have a vast range of possible values for the cosmological constant, without any first principles to force its value. By reasoning that has come to be known as the anthropic principle, they argued further that we necessarily live in a universe with a cosmological constant that is capable of supporting life like us, and so we shouldn’t seek any deeper explanation for it. A big debate
transpired in the cosmology and string theory community as to whether the anthropic principle was scientific. I decided to take another direction, which would risk further shunning from my colleagues. This new direction would mean that I would engage in conversations with the outsiders from my club and even import their ideas into a possible resolution of the cosmological constant problem. I was guided by the motto: “Let the nature of the problem dictate the tools you should resort to,” even if it meant borrowing from the outsiders or risk becoming one yourself. Active deviance was on the horizon.

  That I even wanted to work on the cosmological constant problem was already deviant behavior. In the aftermath of that paper, postdocs were warned to not work on it. Some of my advisers suggested that we postpone working on the cosmological constant until we got tenure. It was a Medusa that defeated the morale of many theorists who attempted to decipher one of nature’s biggest puzzles. But I was haunted by the beauty of the cosmological constant problem and was fine with joining the ranks of those that it defeated. Plus, it was my last year on the job market for a faculty job, and I did not have high expectations of getting a permanent position, so I did not feel like I had much to lose.

  If there was any chance to tread forward, I would have to find a new direction that was not thought of before. One day while having coffee on top of a hill in Nob Hill, I saw a similarity between the cosmological constant problem and a problem that haunted particle physics, the strong CP problem that came up in baryogenesis and the origin of our matter-filled universe. In the strong nuclear interaction, described by a theory otherwise known as quantum chromodynamics (QCD), the gluon is the particle that mediates the interaction between quarks that bind to neutrons and protons. Classically the neutron is electrically neutral, but quantum effects induced by QCD create a very large amount of net electric charge in the neutron that would destroy the stability of atoms. This would be catastrophic, given that we’re made up of neutrons and protons. Like the cosmological constant in general relativity controlling whether the universe expands, is stable, or contracts, there is a parameter in QCD, called the theta parameter, that controls the amount that the neutron deviates from electrical neutrality. Experimentally the theta parameter was measured to be on the order of one billionth. So, the strong CP problem is relegated to a question as to why the theta parameter was so close to zero, a similar predicament as the cosmological constant.

  In the late seventies, Helen Quinn and Roberto Peccei found an elegant solution to the problem. They realized that the strong interactions could have a hidden new symmetry. Think of this symmetry like a particle rotating around a frictionless surface in a perfect circular orbit. If all forces were absent, every point of the ball’s orbit would have the same energy. So, the energy has a symmetry such that any rotation of the ball leaves the energy invariant. Now if we add gravity to the problem and slightly tilt the circle, then the gravitational force would break the symmetry, simply because there is potential energy in the gravitational force. Similarly, Peccei and Quinn showed that a quantum effect—the emergence of a new field called the axion—breaks CP symmetry, introducing a potential energy. This axion readjusts itself to the minimum of the potential and conspires to drive the theta parameter to zero. I wondered if we could reimagine the cosmological constant to act like the theta parameter of gravity. Luckily, Helen Quinn was at SLAC. I told her the idea once over lunch.

  We sat at a work desk in her office and Quinn meticulously walked me through the conceptual and mathematical inner workings of her solution to the strong CP problem. There is a big difference between reading a research paper on a physics result and learning it directly from the author herself. It was only when I saw how Quinn thought about the strong CP problem and her and Peccei’s ingenious insight into the solution that I was able to continue to find a way to implement the idea into gravity and the cosmological constant problem. Most importantly, while Quinn had high standards for the creative and technical implementation of the idea, she was encouraging, and it empowered me to take the next step.

  To take the analogy between a problem in QCD and gravity to a place where I could attempt to do a calculation, it would help if I could place gravity on similar footing with QCD, and there was one activity of research that already did that. In the arena of quantum gravity, string theory is seen as the only game in town, but it isn’t. There are other attempts to quantizing gravity, even if they do not sit well with my string theory friends.

  One particular approach is loop quantum gravity (LQG), in which the starting point is to quantize gravity using the same methods as QCD. This possibility came from Abhay Ashtekar’s ingenious insight to rewrite general relativity using variables identical to QCD.3 The idea required me to use the Ashtekar formulation of gravity in the presence of a cosmological constant. When I spoke to the other postdocs about loop quantum gravity, many of them dismissed the theory as “loopy” and suggested that anyone that would work on that theory does not know physics. But I already felt like an outsider and pursued loop quantum gravity anyway. Besides, when I pressed some members of the group to provide a solid critique about loop quantum gravity rather than just make fun of it, most of them did not know the theory well enough to tell me why they thought it was wrong. So, I decided to invite one of the founders of loop quantum gravity, Lee Smolin, to come to Stanford and SLAC to give some lectures on the theory. That way at least we could have a more informed critique of the theory as a group, and I could make progress on my idea for the cosmological constant. I finally learned enough about the Ashtekar formulation to get going on the project. But my invitation to let an outsider come into our club to teach us something left a bad taste in the mouths of members of my group.

  That was just one of the reasons I spent much of my time at a café called Cup of Joe near the top of Nob Hill performing calculations on the project. I would frequently drop by the office of my adviser, Michael Peskin, to discuss my work when I got stuck. Finally, I finished the project and provided a mechanism to partially solve the cosmological constant problem in a manner similar to the Peccei-Quinn mechanism. The key idea is that there is a new axion that, like a person wobbling on a high wire, can readjust itself to cancel the cosmological constant. The model still needed more improvement to address the other aspects of the cosmological constant problem. However, my results were enough to put the paper up for publication, and the idea inspired a new way to think about resolving the disastrous production of dark energy.

  The paper, entitled “A Quantum Gravitational Relaxation of the Cosmological Constant,” was posted on ArXiv.org, a website where physicists share drafts of their papers with the global physics community. Days of silence from the community went by. I was not offended. My office mate, string theorist Amir Kashani-Poor, returned after giving a seminar at the University of Texas at Austin. He told me with a look of awe that he had been lunching with the string theorists, and Steven Weinberg had joined the group. Weinberg shared the Nobel Prize with Abdus Salam and Sheldon Glashow for unifying the electromagnetic force with the weak interaction and is known as a straight shooter. Kashani-Poor told me that Weinberg pulled my paper from his inside sport jacket pocket and said to the group, “Have any of you seen this paper? It looks really interesting.” This was especially vindicating since Weinberg wrote a seminal masterpiece on the various problems with the cosmological constant and the attempts to solve it. Weinberg’s work also provided concrete criticisms and no-go theorems that ruled out many attempts to solve the cosmological constant problem. Luckily my model was able to evade Weinberg’s no-go theorem. My model is still a work in progress, and my research group and I are still improving it to confront how the cosmological constant is related to the onset of dark energy today.4

  This was my first step toward really working on quantum gravity. Aside from the sort of aesthetic question I raised earlier in the book about the big bang—why should gravity only be partially quantized?—there are also pragmatic scientific reasons to seek a quantum theory
of gravity. Currently, there are a handful of unsolved issues at the interface of quantum field theory and classical gravity. And many of these problems find a home in the beginning and early evolution of the universe when both gravitational and quantum physics are expected to be active. These cosmological problems, such as the origin of matter over antimatter, inflationary versus cyclic universes, dark matter and dark energy, are so daunting that they compelled me to deviate again and carry out research in both superstring theory and loop quantum gravity. My collaborators and I have spent the last two decades using these cosmic conundrums as a compass to test and further develop theories of quantum gravity.

  Both LQG and string theory have their own communities, and there are strong feelings about the veracity of each approach. Both have complementary strengths and weaknesses, ranging from technical to conceptual challenges. My take is that both theories provide tools and new concepts to address the unresolved problems facing cosmology and particle physics, and both may not be sufficient. It has always been my take to let the problems and unexplained observations dictate which theories and tools to resort to. Thus, I have had the fortune to use both LQG and string theory in my research. While we have a handful of candidates for quantum gravity, none are complete. It is my view that they are all parts of the elephant, and we can use these approaches to teach us something about what the final theory might look like.

  11

  A COSMOLOGIST’S VIEW OF A QUANTUM ELEPHANT

  We don’t have to get to some altered state of mind or enter a wormhole to see how mysterious the universe is—it’s right in front of our faces. Our electronic devices are controlled by quantum effects of electrons, and yet, we still don’t have a clue about what the ghostly electron is doing as it approaches the two open holes in the double slit experiment. It does something, but whatever it does, it seems like our mind’s eye is unable to visualize or conceptualize it. The uncomfortable picture is that the electron behaves like a wave when we are not looking at it, and not just a material wave but a wave of potentiality—it’s as if some invisible puppet master is playing tricks on us. If we try to interrogate the electron at the two open slits, where we expect it to be doing its witchcraft, it goes back to behaving like a particle, and the interference pattern is lost. Another equally weird situation is when two spinning electrons are entangled and separated at far distances. We still don’t know how one electron can instantaneously know that the other’s spin was measured to always have the opposite spin of its distant partner. Quantum theory predicts this spooky action at a distance but refuses to tell us how it happens. In other words, the math says that the spins should know about each other at infinite distances, but the math doesn’t simply provide a mechanism. These unresolved issues in quantum foundations have led some physicists, including Einstein himself, to believe that quantum mechanics is incomplete. However, as far as precision experiments can tell, all the predictions of quantum mechanics, no matter how bizarre, have been confirmed.