Should scientists be embarrassed that they can’t settle on a definition for the Big Bang? The cosmologist Will Kinney describes it as the “physical theory of the hot infant universe,” while Wikipedia goes for the more elaborate “a physical theory that describes how the universe expanded from an initial state of high density and temperature.” The first refers only to early times, while the latter seems to extend to subsequent times as well. The physicist and science writer Tony Rothman offers the pithier “the universe’s origin,” the theoretical physicist Thomas Hertog suggests that it is the “primeval state” of cosmic history, and a NASA website gives us “the idea that the universe began as just a single point.” These seem to refer to one moment at the start of things, rather than the universe’s life since then.
All of these sources (except NASA, unfortunately) capture something correct. The confusion stems both from the inherent ambiguity of using ordinary language to describe novel scientific concepts and from the state of modern cosmology itself. Cosmology is the study of the universe on the largest scales. So it ignores details of stars and planets, focusing on galaxies and even bigger structures, up to the universe as a whole. Modern cosmology is only about a century old, as it wasn’t until the 1920s that astronomers determined that our own Milky Way is just one of a large number of galaxies and the origin and evolution of them all could be studied together. And it wasn’t until the 1990s that the field matured into the one that exists today, featuring precision measurements and ultralarge datasets.
Dealing as it does with some of the most profound questions about the nature of the cosmos, cosmological research has always involved a vigorous give-and-take between rampant speculation and unanticipated discoveries. Its practitioners have long been fond of spinning purportedly inviolate physical principles from their personal intuitions about how reality should work. But cosmology remains an empirical science—a cherished belief can be quickly swept away by a solid measurement.
The present moment in the science of cosmology is one of consolidation, as we have successfully incorporated the lessons of some impressive discoveries made near the turn of the twenty-first century. Yet crucially important questions remain unanswered, especially about what exactly happened at the onset of the expanding space that evolved into our contemporary universe. It is therefore a good time for books that take stock of where we are and what might come next, and that illustrate which puzzles modern physicists choose to take seriously.
This much we know: we live in a galaxy, the Milky Way, containing around 200 billion stars. There are something like a trillion galaxies in our observable universe, distributed almost uniformly through space. Stars and galaxies condensed out of an originally nearly smooth distribution of matter. Distant galaxies are moving apart from one another. Extrapolating backward, we reach a hot, densely packed configuration about 13.8 billion years ago. We can observe the remnants of this early period in nearly uniform cosmic background radiation coming from every direction in the sky.
The Big Bang model is precisely this general picture, of a universe that expands and cools out of a smooth, hot primordial state. It is well understood and almost universally accepted among modern cosmologists. The Big Bang event is a hypothetical moment when the whole thing might have started, at which the temperature and density are supposed to have been literally infinite—a “singularity,” in physics parlance. This is why the NASA definition above is unambiguously wrong: the Big Bang event has nothing to do with “a single point” in space—it refers to a moment in time.
Nobody knows whether there actually was such an event. To be honest, there probably wasn’t. Einstein’s theory of general relativity predicts that such a singularity would have happened, but most physicists think this signals a breakdown in the theory rather than being an accurate description of the physical world. A prediction of infinitely big physical quantities is apt to be a sign that we don’t have the right theoretical understanding.
Space and time were unified into space-time in 1905 by Einstein’s theory of special relativity, and ten years later he incorporated the force of gravity to make his theory of general relativity. His fundamental insight was that gravity shouldn’t be thought of as a force propagating within space-time, like electromagnetism or the subnuclear forces, but as a feature of space-time itself—in particular its curvature. Matter and energy cause space-time to warp, that warping pushes them around, and we interpret this pushing as the action of gravity.
Over the last century general relativity has proved enormously successful, predicting and accounting for such diverse phenomena as gravitational waves and the existence of black holes. One such success was the prediction that the universe itself does not act as a fixed background but rather expands or contracts. When Einstein first proposed his theory this seemed like an outlandish prospect and one that conflicted with what astronomers had actually observed about the universe. So a couple of years later he suggested a way to fudge it, the “cosmological constant,” representing a fixed amount of energy inherent in the fabric of space-time itself. This new ingredient in the cosmic cocktail would push the universe apart, counteracting the pull of ordinary gravity and leading to a perfect balance that could keep the universe static.
It’s easy for us to say—and people have—that Einstein should have stuck his neck out and predicted a universe that is either expanding or contracting. As it happened, Edwin Hubble and others showed in the 1920s that distant galaxies are moving away from us, exactly as we would expect if the universe is expanding, and the cosmological constant was abandoned as a short-lived wrong turn. And then, because the universe appreciates irony, in 1998 astronomers discovered that the expansion of the universe is accelerating. The simplest explanation for this is that the cosmological constant is real after all, but it contributes to pushing the universe apart rather than helping it balance at a fixed size.
To be safe, since we’ve verified the acceleration but aren’t completely sure that Einstein’s cosmological constant is the correct explanation, cosmologists use “dark energy” to refer to whatever substance is speeding up the universal expansion. This intentionally parallels “dark matter,” an invisible matter-like substance that can’t be any known particle but whose existence is confirmed through its gravitational pull on galaxies and light rays. Altogether we have a picture in which about 5 percent of the energy in the universe comes from “ordinary” matter (the kinds of particles we’ve detected here on Earth), 25 percent from dark matter, and the remaining 70 percent from dark energy.
One other big discovery occurred around the year 2000 when a series of observations by satellites and radio telescopes mapped the temperature pattern of the cosmic microwave background, the leftover radiation from the high-temperature early universe. This radiation looks almost the same in every direction in the sky, but not quite. Its temperature varies in tiny ripples of about one part in 100,000 from place to place. By analyzing statistical patterns in these ripples, cosmologists were able to verify that the 5/25/70 mixture of ordinary matter/dark matter/dark energy is indeed on the right track. That overall picture has become the standard cosmological model, and astronomers are putting considerable effort into further refining and testing it.
This situation raises an issue for any book that hopes to introduce a nonspecialist to modern cosmology. There are basic features that have been firmly established: Einstein’s general relativity, a largely uniform universe expanding from an initially hot and dense state, structures forming under the influence of gravity, and a combination of dark matter and dark energy or some appropriate substitute for them. Yet serious unanswered questions remain. What precisely happened in those early moments 13.8 billion years ago? What exactly are dark matter and dark energy? More speculatively, does the apparent uniformity of our universe continue beyond the part we can observe, or is there a wildly varying “multiverse” out there? Not to mention more philosophical questions such as why the universe has the particular qualities it does, or even why the universe exists at all. Any book must decide how to balance a review of what is established against a survey of possible answers to the remaining questions, and also whether to weigh in on any controversies.
The three books under consideration take very different approaches. Tony Rothman’s A Little Book About the Big Bang, as the modest title may suggest, concentrates on well-established aspects of the standard picture rather than lingering on open questions. It provides an accessible and engaging overview of modern cosmology for anyone who is not especially familiar with the subject.
Rothman is a physicist best known for his science writing. He is clearly practiced in conveying difficult ideas without jargon, and his book is a model of craftsmanship. It elegantly explains the basics of relativity and the expanding universe, the early universe and the microwave background, dark matter and dark energy, and the formation of stars and galaxies. A Little Book is not, of course, the first to attempt to explain gravitation and cosmology to a wide audience, and Rothman helps himself to a number of traditional explanatory strategies. These include some that are more misleading than helpful.
For example, he indicates that the theory of general relativity, which states that gravitation is due to the curvature of space-time, came about because Einstein wanted to “include accelerations” in special relativity. But special relativity is perfectly capable of handling accelerated motion without any mention of gravity or curvature. (It would be a feeble physical theory indeed that was incapable of describing accelerated motion—just a bunch of particles moving forever in straight lines, never bumping into or otherwise influencing one another.) As a matter of history, Einstein thought a lot about acceleration while he was developing general relativity, but the final product doesn’t say anything especially new about it. The distinction between special and general relativity is the presence or absence of gravity, not acceleration. Special relativity features a rigid, flat space-time background (initially parallel rays remain parallel), while in general relativity space-time is curved (initially parallel rays can converge, diverge, or twist around). A small point, perhaps, but these kinds of misrepresentations add up.
Near the end of the book Rothman turns to the theory of cosmic inflation, a subject where detailed experimental predictions and wildly unconstrained speculations go hand in hand. Inflation, first popularized by Alan Guth in an influential 1981 paper, is a curious kind of scientific idea. It is not meant to replace a specific alternative theory or to reconcile a disagreement between prediction and data. Rather, it is meant to show how certain apparently puzzling features of our universe are actually perfectly natural.
Guth highlighted three features in particular. One is the “horizon problem,” which stems from the fact that conditions in widely separated parts of the early universe, as observed in the temperature of the microwave background in different parts of the sky, are remarkably similar. That implies that they must have started expanding at the same time. But this is difficult to understand in relativity, since the regions in question seem to be so far apart that a light ray from one wouldn’t have had time to travel to the other by the time the background radiation was formed—they were outside each other’s “horizons.” And relativity says that nothing travels faster than light. So how did these regions know to start expanding at the same time, if they could never have exchanged information?
A second issue is the “flatness problem.” Einstein tells us that four-dimensional space-time is curved, but we can separately ask about the curvature of three-dimensional space at any one moment in time. That curvature is very small on human scales, which is why ordinary Euclidean geometry works so well. But the universe could plausibly be dramatically curved. Moreover, the equations of general relativity predict that any overall curvature at early times would grow relatively larger and more noticeable as the universe expanded. Yet when we observe our current universe, there is no apparent curvature to be detected—space seems flat, or close to it, on cosmic scales, which means it must have been very flat at early times. Why is the universe flat if it could easily have been curved?
Finally, Guth addressed the “monopole problem.” Physicists have understood electric and magnetic fields since the nineteenth century. There is an important distinction between them: individual particles can have a single electric charge, like a positively charged proton or a negatively charged electron, but magnets always have both a north pole and a south pole. They are dipoles, not monopoles. But ambitious attempts to unify the fundamental forces, known as grand unified theories, seemed to predict that there should be magnetic monopoles in the universe; indeed, they should exist in such abundance that the universe should contain little other than such monopoles, which is clearly false. Where did all the predicted monopoles go? This third problem arises only for fans of grand unified theories, which have lost a bit of luster over the decades (though some version of grand unification might ultimately turn out to be on the right track). But the horizon and flatness problems seem to be robust issues for cosmology.
Inflation offers a simple solution. Just as our universe is accelerating today because of dark energy, we imagine that a superdense kind of dark energy dominated the universe at very early times, leading to rapidly accelerated expansion for a short period, until that temporary energy converted into ordinary matter and radiation. Inflating the universe is like pulling on the edges of a wrinkled sheet, smoothing it out and leaving it flat. And unwanted magnetic monopoles are efficiently “inflated away,” leaving us with just the kind of universe we live in today.
The inflationary universe scenario was an immediate hit among theoretical physicists, but more observationally oriented astronomers remained skeptical for a couple of decades. That changed around the turn of the century, thanks to the experimental discoveries of dark energy and ripples in the cosmic microwave background. The former provided just enough energy to account for the flat geometry of space, as inflation had predicted. The latter gave strong evidence that the fluctuations in density that grew into galaxies and larger structures were baked into the universe at early times, another prediction from inflation. Today inflation is the dominant paradigm through which cosmologists think about the early universe.
But the idea of inflation, as elegant as it might be, remains speculative. It requires a source of ultradense dark energy, provisionally labeled the “inflaton field,” whose identity remains mysterious. Cosmologists consider a wide variety of different specific models under the umbrella of inflation, and a great deal of effort is currently going into winnowing those models through comparison with ever-more-precise observations of the microwave background and the statistical properties of galaxies and large-scale cosmic structure.
Rothman’s book mentions this ongoing cosmological research without going into specifics. Those specifics are the central focus of Will Kinney’s short book, An Infinity of Worlds: Cosmic Inflation and the Beginning of the Universe. Kinney is a working cosmologist who specializes in the connection between inflationary models and astrophysical observations. His book is very good at explaining how those connections come to be.
It’s a fascinating story. Guth’s original idea was simply to account for the apparent unnaturalness of our flat, smooth, monopole-free universe. But it was soon recognized by a number of physicists that inflation wouldn’t leave the universe perfectly smooth, thanks to the undeniable importance of quantum mechanics.
Quantum mechanics is sometimes portrayed as a theory that describes the smallest of objects, but that’s not quite right. Quantum mechanics describes everything, up to and including the universe itself. It’s just that we usually don’t notice the differences between quantum and ordinary classical mechanics until we start considering individual atoms and particles. But in certain circumstances, including the earliest moments of cosmic history, the features of quantum mechanics become centrally important.
According to Werner Heisenberg’s uncertainty principle, the position and velocity of a quantum system cannot be simultaneously specified with perfect precision. All systems are subject to tiny “quantum fluctuations,” whether we’re considering single electrons or the universe as a whole. For macroscopic objects like a baseball or a planet, those fluctuations are negligibly small, so we might imagine the same would hold for the entire universe. But our currently observable universe could easily have been smaller than a single atom during the inflationary era, so quantum effects become important.
Take that basic idea, apply it to a specific model of the inflaton field and its dynamics, and you end up with a quantitative prediction for ripples in matter density that will imprint on the temperature of the cosmic microwave background and ultimately grow into the galaxies we see today. Kinney’s book explains the underlying physics with an appropriate degree of detail and without becoming overly technical, and it should be welcomed by cosmology enthusiasts for that reason.
This doesn’t quite account for the title of the book—what is this infinity of worlds? It is here that things get dicier. As Kinney explains, the very same quantum fluctuations that seem to successfully account for the large-scale structure of our universe also have an unintended consequence known as “eternal inflation.” The idea is that, while the inflaton field may ultimately convert into ordinary matter and radiation across most of space, there’s a chance that in some particular region a quantum fluctuation keeps the field at high energy for longer. That region inflates and therefore grows much larger. The process then repeats, so that there is always some inflation going on somewhere, even as much of the universe settles into a more recognizable hot-Big-Bang phase.
Eternal inflation is the origin of the idea of an infinity of worlds. As inflation ends in one region after another, while continuing elsewhere, these regions can be thought of as essentially different universes, separated by such enormous distances that they can never interact with one another. The resulting ensemble is the cosmological multiverse.
The multiverse is either a bug or a feature, depending on your perspective. Inflation has a somewhat unusual status as a scientific theory. The conventional Big Bang model is in complete agreement with the data; all we have to do is specify the correct initial conditions, which physicists do all the time. The problem that motivated the idea of inflation was not that we couldn’t think of any initial conditions that do the job, but that the ones that work—spatial flatness, uniformity over large scales, particular kinds of small but crucial perturbations—seem unnatural to us. They seem delicate; small variations from a certain precise set of initial conditions would have resulted in a very different universe. Inflation was intended to provide a way for a relatively simple initial condition—a tiny patch full of high-energy inflaton field—to naturally lead to a universe much like ours.
And now we’re being told that inflation doesn’t actually do that; it leads to a multiverse of infinite possibilities. Some parts of the multiverse will in fact resemble what we see around us, but others will look completely different. You might hope that most regions would appear familiar to us, but it turns out to be a challenge to make sense of what “most” means in this context. Eternal inflation creates an infinite number of universes, and they can all be somewhat different from one another, so every allowed universe happens an infinite number of times. How do you talk about what is most probable in such a situation? This is the “cosmological measure problem,” which has been addressed in various ways, none completely convincing.
Some physicists, such as Roger Penrose, Paul Steinhardt, and Anna Ijjas, have argued that eternal inflation renders the entire inflationary paradigm unscientific because it can’t predict anything. Others bring up a famous idea from the philosopher of science Karl Popper, that a theory isn’t scientific unless we can imagine an experiment that would, if the results came out a certain way, falsify the theory. Eternal inflation predicts a panoply of different universes surrounding us, but we can’t perceive or interact with them, so there’s no way to falsify the idea that they are there. Popper’s criterion isn’t especially popular among contemporary philosophers of science, but it has a grip on the imaginations of many working scientists.
Alternatively, we can take the inflationary lemons and turn them into lemonade. Many cosmologists have come to think of the multiverse as a solution to otherwise intractable problems. In some models, the resulting universes can look very different indeed, including having different apparent “constants of nature.” We can then invoke the anthropic principle: if conditions vary widely across a collection of universes, intelligent life (such as ourselves, presumably) will observe only the subset of conditions that are compatible with the existence of intelligent life. This trick can be used to account for features of cosmology and physics that seem unnatural or finely tuned; if things were otherwise, we wouldn’t be here to talk about them.
Kinney doesn’t like any of this. He nicely explains the physics of eternal inflation and the associated cosmological measure problem. He even notes that eternal inflation is hard to avoid if we want to accept inflation at all. But he rejects the anthropic principle as unscientific, on the grounds that the other universes are unobservable. What’s unclear is what we’re supposed to do about the situation.
To be fair, this is a problem for much of modern cosmology, and one that is discreetly ignored more often than it is directly addressed. Contemporary cosmologists frequently act as if inflation were all but established and work diligently to connect observable features of the cosmic microwave background and the distribution of galaxies to specific inflationary models. They pay little attention to the problem that the same models seem to predict completely different features elsewhere in the multiverse. Some of us are optimistic that this issue can be successfully addressed, but at the moment there is too much we don’t know about the early universe, quantum gravity, and how to deal with infinity.
The multiverse isn’t the only skeleton lurking in the inflationary closet. The entire point of inflation is to explain why the early universe looks the way it does. But why would the early universe find itself in a state that would lead to inflation in the first place? Penrose, among others, has convincingly argued that as unlikely as the early universe might seem in the conventional Big Bang picture, an inflationary beginning is less likely still.
This starting-out problem and the multiverse puzzle are the focus of Thomas Hertog’s On the Origin of Time: Stephen Hawking’s Final Theory. It’s much more cheerfully speculative than Rothman’s and Kinney’s books, zipping quickly through established cosmology in order to dive into the deepest possible waters. Hertog graces the reader with frequent historical anecdotes and philosophical disquisitions, which are of intrinsic interest, though they also work well to break up the heavier passages on physics.
The name of Stephen Hawking, who died in 2018, is undoubtedly a box office attraction, but it deserves its place in the title. Hertog is a prolific physicist who was a graduate student of Hawking’s, and they remained frequent collaborators. Not long after Guth’s proposal of inflation, Hawking and his coauthor James Hartle inaugurated quantum cosmology, the study of the entire universe as a quantum system, space-time included. Hawking and Hertog, often with Hartle (who died in 2023), continued to develop this approach, and their most recent work provides the through line for this book.
The results are scientifically and philosophically engrossing, although only a mixed success pedagogically. These ideas are tricky. Hawking and Hertog propose to take the conventional way of dealing with a cosmological multiverse and turn it on its head, via what they call “top-down cosmology.” Rather than surveying a vast cosmos and asking where we might find ourselves within it, they start with our observable situation and ask what that implies about the larger quantum state of the universe. This shift of perspective, Hertog claims, helps resolve the usual problems with the multiverse, while reinstating the primacy of the particular history that led us to the universe we find ourselves in today.
It is difficult to evaluate this proposal, in part because it has not matured into a rigorously defined paradigm with unambiguous empirical consequences. Hertog has clearly put enormous effort into explaining these ideas, but some of them remain hard to understand at the level of a nonspecialist discussion like this one. The book is nevertheless extremely rewarding, capturing some of the excitement of big-picture research along with insight into Hawking’s unique character. At Hertog’s very first meeting with his future doctoral adviser, Hawking asked him, “Why is the universe the way it is? Why are we here?” As Hertog muses, “None of my physics teachers had ever spoken about physics and cosmology in such metaphysical terms.”
Taken together, these three books provide an illuminating view of the state of modern cosmology. There are established results, laudable efforts to connect promising hypotheses to a flood of incoming data, and brave speculations about the physical and metaphysical unknown. They are all notably well written for the genre and will keep readers entertained as they are educated. We can marvel at both how much scientists have learned about the universe and how much we have yet to understand.
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