String theory poses a challenge cosmologists can't sleep over
Inflationary cosmologists face a serious theoretical challenge stemming from string theory that has become a source of deep unease in the field. The piece explores the foundational question of where the universe ultimately comes from, tracing cosmic history from the hot dense early state through dark matter, dark energy and large-scale structure formation. String theory's implications may undermine key assumptions of the inflationary cosmological model.
Perhaps the biggest existential question we’ve learned how to ask is one of the most straightforward ones of all: the question of, as you look around at our world, galaxy, and cosmos, where it all ultimately comes from. Sure, we can look back — farther through space and further back in time — and learn about our cosmic past. We can learn about the evolution of chemical elements and the birth of planets, we can learn about the cosmic star-formation history and the growth of galaxies and large-scale structure, and we can learn about the hot, dense, uniform state that preceded everything we observe today. We can learn how the ingredients within our Universe, including normal matter, dark matter, dark energy, photons, and neutrinos, shaped the expansion history of our Universe, and allowed minuscule seeds of structure to grow into today’s star-and-galaxy-rich cosmic web. We can trace our cosmic history back not only to the hot Big Bang, but to an inflationary state that preceded it and set up the Big Bang with the right properties to reproduce and create the Universe as we observe it all throughout cosmic history. But despite all of these successes, we only have access to information from the final 10-32 seconds or so prior to inflation’s end. Questions about its total duration, about its origin (if it had one), and about a pre-existing state that gave rise to inflation remain unanswered. Even though it’s only suggestion and speculation, there’s a set of thoughts about our ultimate cosmic origins that, when you put them together, point in a very stringy direction. Here’s why even those who are the most skeptical of string theory can’t dismiss its importance when it comes to the very beginning of our Universe. The central idea of string theory is that all the quanta we know of are described by tiny strings that vibrate in various ways on minuscule scales: far below what’s ever been probed. String theory is an attempt at a framework for quantum gravity, and arguably the only viable candidate for finding out what’s real in the Universe on trans-Planckian scales. Credit: Berkeley Center for Cosmological Physics Simply by looking back through space, we can see the Universe as it was further back in time. When we take stock of what we find back then, some fascinating features include: a cosmic microwave background that was hotter in temperature, a Universe that was less clumped and clustered, with smaller, lower-mass galaxies and galaxy clusters, with populations primarily of younger, bluer, and less chemically enriched stars, where the Universe was denser, and where the expansion rate was greater in the past, all of which point to the same early picture of our cosmic origins: the hot Big Bang. By hypothesizing an early hot, dense, nearly uniform, rapidly expanding, matter-and-radiation filled state, we can make sense of the evolution to the cold, sparse, heavily clumped and structure-rich, slowly expanding, dark energy and dark matter-dominated Universe that we observe today. However, this picture itself, of the hot Big Bang, doesn’t explain everything that we observe about the Universe. It doesn’t explain why the energy density and the expansion rate seem to balance one another so perfectly: the flatness problem. It doesn’t explain why different regions of ultra-distant space, including in opposite directions from one another, have the same temperature as one another: the horizon problem. It doesn’t explain why there are no leftover high-energy relics, as one would expect, from an arbitrarily hot, dense, early state: the monopole problem. And it doesn’t explain what the seeds of our large-scale cosmic structure would need to be, or provide a mechanism for creating them. In the top panel, our modern Universe has the same properties (including temperature) everywhere because they originated from a region possessing the same properties. In the middle panel, the space that could have had any arbitrary curvature is inflated to the point where we cannot observe any curvature today, solving the flatness problem. And in the bottom panel, pre-existing high-energy relics are inflated away, providing a solution to the high-energy relic problem. This is how inflation solves the three great puzzles that the Big Bang cannot account for on its own. Credit: E. Siegel/Beyond the Galaxy These motivating factors are what led scientists to concoct and develop the idea of cosmic inflation during the late 1970s and early 1980s. According to inflation, the Universe didn’t begin from an arbitrarily hot, dense state, where all of the matter and energy in the Universe was compressed into a single point — a singularity — at an event that marked the birth of space and time. Instead, if you rewound the clock back to early enough times, to a hot-and-dense state that was still of a finite size, volume, and temperature, you’d find: That instead of being filled with matter-and-radiation, the Universe was filled with field energy, or energy inherent to space itself. That instead of expanding and cooling, the Universe was expanding at a constant, relentless rate: doubling in size again and again with each small interval of time that elapsed. That the Universe’s entropy remained constant during this phase, but due to the relentless expansion, its entropy density plummeted. That no matter what the conditions of the Universe were prior to inflation, inflation had now stretched it flat, and imbued it with the same temperatures and densities everywhere. And that because there are still quantum fields in the Universe, as inflation goes on and on over time, those fluctuating quantum fields get stretched across space to all scales, leading to a spectrum of “seed fluctuations” that will translate into energy density (and temperature) fluctuations when inflation comes to an end. That last fact is a key prediction of inflation, as it allows us to build inflationary models that possess specific fluctuation spectra: spectra that then translate into CMB fluctuations and features in the large-scale structure of the Universe that we can, in the here-and-now, go out, test, and measure. The fluctuations in the cosmic microwave background, as measured by COBE (on large scales), WMAP (on intermediate scales), and Planck (on small scales), are all consistent with not only arising from a (slightly tilted, but almost-perfectly) scale-invariant set of quantum fluctuations, but of being so low in magnitude that they could not possibly have arisen from an arbitrarily hot, dense state. The horizontal line represents the initial spectrum of fluctuations (from inflation), while the wiggly one represents how gravity and radiation/matter interactions have shaped the expanding Universe in the early stages. Credit: NASA/WMAP science team Inflation can help explain not only the flatness, horizon, and monopole problems, but it makes additional, explicit predictions that have now been verified: that the nature of the seed fluctuations would be entirely adiabatic (and not isocurvature), and that there would be seed fluctuations that existed on super-horizon scales, which remains some of the strongest observational evidence that favors and validates cosmic inflation. Additionally, the models of inflation that work to describe our Universe are the ones that: produce a maximum temperature, for the hot Big Bang, that’s at least a factor of several thousand smaller than the Planck temperature, produce a spectrum of almost scale-invariant fluctuations, but with fluctuations that are about 3% greater on large cosmic scales rather than small ones, produce only very small-magnitude gravitational wave (tensor) fluctuations, and that lead to the magnitude of initial temperature/density fluctuations being at about the few-parts-in-100,000 level, with respect to the average cosmic temperature/density. From that initial set of seed fluctuations — a spectrum of fluctuations predicted and produced by inflation — normal and dark matter gravitate, radiation pushes back on the normal matter, and we get temperature imperfections that imprint themselves in the cosmic microwave background, and then later, correlations between galaxies in the resultant large-scale structure of the Universe. A detailed look at the Universe reveals that it s made of matter and not antimatter, that dark matter and dark energy are required, and that we don t know the origin of any of these mysteries. However, the fluctuations in the CMB, the formation and correlations between large-scale structure, and modern observations of gravitational lensing all point toward the same picture. Credit: Chris Blake & Sam Moorfield That’s the short version of the story of cosmic inflation and how it leads to the Universe we observe today. No alternative to inflation has reproduced these successes, while inflation has made many predictions that differed from the hot Big Bang without inflation, all of which have fallen in favor of inflation wherever they’ve been tested. It’s one of the most spectacular theoretical and observational successes of a theory in the late 20th and early 21st centuries. And yet, inflation doesn’t tell us everything. Because of its very nature — the fact that, during that early period of inflation, it caused empty space to double again and again, relentlessly, with each tiny fraction-of-a-second that elapses — the only imprints we have of inflation that exist within our observable Universe (i.e., inside of our cosmic horizon) were created during the final 10-32 seconds of inflation. In other words, anything that happened prior to inflation’s final moments, including: anything that led to a change in inflation’s behavior, anything that caused the onset of inflation in the first place or triggered the initiation of an inflationary state, or anything that pre-existed in the Universe prior to those final moments of inflation, has forever been erased from the portion of our Universe that’s even in principle observable to us. During cosmological inflation, the space contained in the inflationary region grows exponentially, doubling in all three dimensions with each tiny fraction-of-a-second that passes. Where inflation ends, a hot Big Bang ensues. But due to quantum effects, each region where a Big Bang occurs will be surrounded by more inflating, exponentially expanding space, ensuring that no two regions where hot Big Bangs occur ever collide, intersect, or overlap. Credit: Kavli IMPU Why is that? Because it was wiped out by the very nature of inflation itself. All we have to resort to, in this regime, are mathematical and theoretical arguments, as there is nothing observable or measurable we can point to in order to shed further light on the issue of our cosmic origins before those final moments of inflation. We are capable of learning some lessons from those considerations, however. We learn that inflationary spacetimes are past-timelike-incomplete, which teaches us that the inflationary state could not have been eternal to the past, but rather was preceded by a prior, non-inflationary, and possibly singular (but also possibly non-singular) state. But what was that state? It had to have been a high-energy state, otherwise there’s no way to get the high energy densities that we experience at the start of the hot Big Bang. It may be related to the Bunch-Davies vacuum, which corresponds to a particle-free state in an exponentially expanding Universe. It could correspond to a state of grand unification, where not only were the electromagnetic and weak nuclear forces unified, but the strong nuclear force joined them as well. It’s also possible that there were more dimensions to our Universe during whatever pre-inflationary state our Universe possessed. There’s an important paper from around that key time — right at the border between the late 1970s and the early 1980s — that contained within it a profound and powerful realization. This animation shows three expanding dimensions of space emerging in the Kasner metric from a higher-dimensional spacetime with one contracting dimension. Even though the three expanding dimensions begin anisotropic, as they grow, the portion of the Universe that’s observable will become indistinguishable from flat, homogeneous, and the same in all directions. Credit: Lantonov/Wikimedia Commons That paper, written by Alan Chodos and Steve Detweiler, is simply titled, “Where has the fifth dimension gone?” In the paper, they show that if you start from a five-dimensional Universe, where four of those dimensions are spatial and the other one is a time dimension, and you allow that Universe to be in an empty, vacuum solution state (described by the Kasner metric), then as one spatial dimension shrinks, the other three dimensions grow. What you wind up with, then, is a Universe that’s: isotropic (the same in all directions), homogeneous (the same in all locations), expanding, with three spatial dimensions and one time dimension, and described by the same solution to Einstein’s general relativity that physicists have used for over 100 years to describe our Universe: the Friedmann–Lemaître–Robertson–Walker metric. Think about all of this together, now. We live in a (with three space and one time) four-dimensional Universe. It’s isotropic and homogeneous today, and filled with matter and radiation, after arising from a prior state that was represented by an empty, rapidly and relentlessly expanding past, where quantum effects were important and stretched to cosmic scales. If the energies were great enough, forces could have unified. If there were extra dimensions, their shrinking could provide an explanation for why the three dimensions we have today expanded in the past, and continue to expand today. And if you consider the possibility that gravity was unified along with the other forces — what’s known as a theory of everything — there’s only one known candidate theory that allows you to embed both general relativity and the entire Standard Model fully within it: string (and/or superstring) theory, requiring 10 dimensions in its unbroken, fully restored state. One of the most popular efforts toward a Theory of Everything is string theory, where the Lie Group E8 x E8 is shown here: one realization of 10-dimensional superstring theory. The number of particles, fields, interactions, and dimensions that must be removed to keep the predictions of this overarching framework consistent with what we observe in our Universe is overwhelming, and represents more than 95% of the theory’s general predictions. Credit: Claudio Rocchini & Peter McMullen/Wikimedia Commons This leads to the big thought that sometimes keeps me, as well as other cosmologists who think about the ultimate origins of our Universe, up at night. When you start with a spacetime of a given number of dimensions, there are only a few Lie groups (a certain type of mathematical structure) that can cover them, where every Lie group corresponds to a spectrum of particles, as well as a set of forces and interactions between those particles. For superstring theory in its unbroken state, that 10-dimensional spacetime can be covered by a Lie group like SO(32) or double-covered by E8 ⊗ E8. Both of these groups contain not just the Standard Model and general relativity within them, but a whole host of other things that we know our Universe doesn’t actually possess. In order to get down to just four-dimensional spacetime, however — the spacetime that we observe ourselves to inhabit here in the modern, post-Big Bang Universe — we have to make six of those dimensions go away: a process known as compactification. While some deride compactification as a hand-wavy process, from a mathematical perspective, there are only a few options. 10 dimensions can be broken down into: 5 + 5 dimensions, 6 + 4 dimensions, 7 + 3 dimensions, 8 + 2 dimensions, or 9 + 1 dimensions, with larger numbers of dimensions having the ability to be broken down further. If you examine the “6 + 4” option in detail, however, as having four dimensions is particularly relevant to our Universe, it turns out that while there are many ways for the “6” part to be compactified, there’s only one unique mathematical state to describe the four-dimensional part. If you go from 10 dimensions down to four, the “four” part that emerges is unique. This particle chart shows the pattern of charges W (weak isospin), W’ (weaker isospin), g3 and g8 (strong force charges), and B (baryon minus lepton number) within the SO(10) grand unified theory. The pattern has been rotated to show its embedding within the larger E6 group. Credit: Cjean42/Wikimedia Commons Sure, there are still more particles and more interactions than we have from the plain old Standard Model; the Lie group that (maximally) covers this four-dimensional spacetime is E6, which allows for grand unification to occur, but which contains the entire Standard Model within it: SU(3) ⊗ SU(2) ⊗ U(1). The theory of gravity that describes this spacetime is almost equivalent to Einstein’s general relativity; once we come down to four spatial dimensions, it’s equivalent to a scalar-tensor theory of gravity known as Brans-Dicke gravity. All we have to do is remove the scalar term (or take the Brans-Dicke coupling term, ω, to infinity), and we recover Einstein’s standard general relativity. Sure, there are still puzzles related to this idea: where are the extra particles and interactions predicted by this larger Lie group, why are there no flavor-changing neutral currents seen in particle physics experiments, why haven’t we observed proton decay if the interactions are allowable, and what mechanism effectively “hides” these extra theoretical components that don’t appear to manifest in nature, but the possibility that this idea relates to the origin of our Universe cannot be so easily ignored. If our Universe did indeed emerge from a 10-dimensional string theory, then breaking those ten dimensions down to our four could not only give us our theory of gravity and our Standard Model of particles and interactions, but the process of compactification could lead to a state, for the remaining spatial dimensions, that looks a whole lot like the scenario of cosmic inflation appears to us in our cosmic past. The quantum fluctuations inherent to space, stretched across the Universe during cosmic inflation, gave rise to the density fluctuations imprinted in the cosmic microwave background, which in turn gave rise to the stars, galaxies, and other large-scale structures in the Universe today. This is the best picture we have of how the entire Universe behaves, where inflation precedes and sets up the Big Bang. Unfortunately, we can only access the information contained inside our cosmic horizon, which is all part of the same fraction of one region where inflation ended some 13.8 billion years ago. Credit: E. Siegel; ESA/Planck and the DOE/NASA/NSF Interagency Task Force on CMB research Today, we have a Universe that’s governed by two sets of laws that we understand — general relativity as our theory of gravity, with the Standard Model plus quantum field theory providing the particle content and describing the other three forces — plus a slew of unsolved mysteries, including cosmic inflation, dark matter, and dark energy. Although there are many models for all of these unknowns, it remains possible that they’re all related not only to one another, but to the cosmic knowns as well, and (super)string theory is the one framework that is actually capable of bringing them all together. Of course, none of these problems or puzzles, individually, requires string theory of any variety in order to solve them. Each one can be solved by a much simpler solution. Inflation can be modeled as a single scalar field. Dark matter can be modeled as a single species of cold, collisionless particle. Dark energy could simply be a cosmological constant with a positive, finite, non-zero value. And beyond that, the remaining mysteries that are often discussed today (like the Hubble tension or evolving dark energy) could be mere phantasms: spurious results that won’t require any new physics once better observational data arrives. Still, there’s that nagging thought that persists: what if everything we don’t understand today, or that we can’t explain today, ultimately has the same, single solution that dates back to an epoch in cosmic history beyond the limits of what’s observably imprinted on our Universe? That’s the stringy thought that sometimes keeps inflationary cosmologists up at night. Now that you understand that line of thinking, perhaps you’ll wonder about that same possibility yourself. This article One stringy thought causes inflationary cosmologists to lose sleep is featured on Big Think.
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