Could the birth of a four-dimensional black hole have created our three-dimensional universe?
That’s the idea put forth by the authors of a new paper on the arXiv preprint server1. Traditional Big Bang cosmology aligns well with many of today’s precision astrophysical measurements, they write, but it still leaves some important questions unanswered: In particular, what happened at the infinitely dense point, or singularity, from which the Big Bang sprung?
Artist's impression of a growing supermassive black hole. Image credit: NASA/CXC/A.Hobart
As Niayesh Afshordi, an astrophysicist at the Perimeter Institute for Theoretical Physics and one of the paper’s authors, told Zeeya Merali for Nature News, “For all physicists know, dragons could have come flying out of the singularity.”
“In the current best theories that we have, we know that we don’t know,” says Sean Carroll, a theoretical physicist at Caltech who was not part of the team that published the new paper. “We have theories of the universe that work really, really well, but they just don’t say anything about the Big Bang. They fail to give an opinion.” And when the equations of general relativity are applied to the Big Bang singularity, they pop out infinite answers. “What that really means is that the equations are breaking down,” explains Carroll.
Many physicists can stomach that breakdown as long as the singularity is quarantined behind an event horizon, an invisible boundary beyond which no information can pass to an outside observer. “If they [singularities] are ‘hidden’ behind event horizons, they do not affect our predictions, and so we can still use laws of standard physics,” says Afshordi. But the Big Bang singularity is not shielded in this way; instead it is what physicists call “naked.”
“’Naked’ singularities are not hidden, and thus anything to the causal future of ‘naked’ singularities will be affected by laws beyond standard physics,” says Afshordi.
Searching for a way to avoid the naked singularity at the Big Bang—and perhaps explain other vexing properties of our universe in the process—the authors of the new paper turned to a model of the cosmos called the “braneworld.” In the braneworld, our observable, three-dimensional universe actually lives inside another universe which has extra spatial dimensions. To use a two-dimensional analogy, our universe is like the skimmable membrane (“brane”) of fat on top of the pea soup of the universe.
We can’t detect this soup, called “the bulk,” directly, but it could explain some bizarre quirks of physics, like why gravity is so much weaker than the other fundamental forces. Yet physicists have not had much to say about what kinds of objects might live in the bulk and how they might affect us here on the brane.
The new paper analyzes what would happen if a black hole formed within the bulk. Unlike a regular old three-dimensional black hole, which is surrounded by a two-dimensional event horizon, a four-dimensional black hole would have a three-dimensional event horizon. And that event horizon would be constantly expanding. Sound like any universe you know?
The paper’s authors argue that this picture could address other mysteries of Big Bang physics, like how the universe settled down to such a uniform temperature so quickly. Physicists typically explain this problem using a phenomenon called cosmic inflation, which is believed to have caused the universe to swell up rapidly soon after the Big Bang. This swift, early expansion means that parts of the universe that seem disconnected today—that is, they are so far apart that they can’t exchange photons—could have “touched” in the distant past.
Inflation has passed nearly every test we’ve put it to. It even matches up nicely with the latest data from the Planck space observatory, which made the most precise map ever of the cosmic background radiation. The new black hole model doesn’t agree as closely with the Planck data. Plus, physicist Paul Halpern points out, “The authors have constructed something that needs to be closely manipulated and tweaked to get the parameters that inflation gets very naturally.”
Halpern also isn’t convinced that the problems the new model sets out to solve are truly so dire. The naked singularity that plagues the equations of general relativity might melt away once we have a theory that combines general relativity with quantum mechanics, says Halpern. The Big Bang singularity “doesn’t really trouble people who think there will eventually be a theory of quantum gravity.” Plus, Halpern points out, there are practical limits on our ability to observe the naked singularity at the beginning of the universe. “As we go back in time, it's harder and harder to make observations.”
It doesn’t seem likely that the Big Bang is going to be dethroned by the Big Black Hole anytime soon. But, says Halpern, “It’s important to be generous in terms of allowing for a wide range of theoretical models. You never know which will help us, ultimately.”
1The paper has been prepared for submission to the Journal of Cosmology and Astroparticle Physics, though it has not yet been peer-reviewed and published.
Author's picks for further reading
arXiv: 4D Gravity on a Brane in 5D Minkowski Space
In this academic paper, physicists Gia Dvali, Gregory Gabadadze, Massimo Porrati propose the brane world scenario on which the new paper is based.
The Nature of Reality: A Journey Into Extra Dimensions
In this video pencast, theoretical physicist Delia Schwartz-Perlov explains what physicists talk about when they talk about extra dimensions.
The Question of Cosmic Censorship
Physicist Roger Penrose on the problem of naked singularities and the possibility that physics may prevent them through “cosmic censorship."
When a team of astronomers in 1992 released the first full-sky map of the cosmic microwave background—also known as the afterglow of the big bang—George Smoot, one of the group’s leaders and later a Nobel laureate, said, “If you’re religious, this is like looking at God.”
Mystical undertones stir passions and risk muddying our understanding of science. But whatever one’s views, it is an intriguing coincidence that a possible key to reading Smoot’s words comes to us from none other than Dante Alighieri’s “Paradiso,” written in the early years of the 14th century. The cosmic microwave background, or CMB, shows us a slice of the universe as it looked more than 13.7 billion years ago, and the structure of that universe bears a striking resemblance to that of Dante’s heaven—at least according to some commentators. It is as if the poet had presaged some of the most striking developments of modern mathematics and cosmology six centuries before they emerged.
“Paradiso,” the third and final part of the “Divine Comedy,” narrates an allegorical journey in which Dante ascends from Earth, visits heaven, and eventually gets to behold the creator himself. First, Dante crosses a series of concentric spheres, all centered at Earth, which hold the planets, Sun, moon, and the stars. The next sphere he reaches is one that encloses the entire physical universe. As he crosses it, he steps into the spiritual realm.
The otherworld however also has a geometric structure, and it is completely symmetrical to that of the physical world, with nine concentric spheres, which are inhabited by angels and the souls of the most virtuous dead. But instead of growing ever larger, these spheres grow ever smaller. And at the center, Dante says, sits God, occupying a single point and emanating a blinding light.
Thus Dante’s entire universe—both physical and spiritual—consists of two sets of concentric spheres, one centered at Earth, the other at God. If you were to point a laser vertically up toward the sky from any point on Earth, you’d be pointing it straight at that single point where Dante places God.
In a sense, then, the successive spheres of the spiritual world enclose all of the physical spheres, Dante seems to imply, even though they get smaller and smaller as you move farther away from Earth and closer to God. Such a geometry seems impossible, and the passage has mystified commentators for centuries. In fact, these bizarrely nested spheres are both mathematically and physically possible. To discover why, we have to turn to mathematics that wouldn’t be discovered until centuries after Dante’s death.
In the geometry of our everyday experience, also known as Euclidean geometry, if we draw a sphere around us, the larger the sphere’s radius, the larger its circumference; more precisely, doubling the radius of a sphere doubles its circumference. But this is an empirical fact and not a logical necessity: there is such a thing as non-Euclidean geometry, in which it is perfectly allowable for a sphere to have a circumference that is not proportional to its radius.
Moreover, non-Euclidean geometry is not just a bizarre, abstract invention of mathematicians. In fact, Einstein showed in his theory of general relativity that the geometry of the universe itself is fundamentally non-Euclidean. This is what allows space to twist and bend like a cosmic contortionist.
The discrepancy between the real world and Euclidean geometry is tiny in ordinary situations—a satellite’s orbit around Earth, for example, may be a few inches shorter compared to what you would expect from Euclidean geometry—but becomes substantial in extreme situations such as around black holes.
Dante’s universe, then, can be interpreted as an extreme case of non-Euclidean geometry, one in which concentric spheres don’t just grow at a different pace than their diameters, but at some point they actually stop growing altogether and start shrinking instead. That’s crazy, you say. And yet, modern cosmology tells us that that’s the structure of the cosmos we actually see in our telescopes.
We can think of the observable universe as being made of concentric spheres, just like Dante’s universe. Because light travels at a finite speed, we see distant galaxies as they were in the past, at the time when they emitted the light that we now receive from them. By definition, light covers one light-year of distance every year. Thus, for example, we can picture all galaxies that we see as they were one billion years ago as residing on a sphere centered at our position and of radius one billion light-years. (These spheres are of course not solid objects, and they not absolute but relative to the observer, contrary to those in Dante’s 14th-century cosmology.)
Now, the universe we see all sprang up from a very small region of space, and has been expanding ever since. Cosmologists have placed the beginning of time at about 13.7 billion years ago. That means that our game of drawing concentric spheres cannot be pushed to an arbitrary distance. But it also has another consequence. As the radius of the spheres pushes close to that magic number of 13.7 billion and change, we are looking at smaller and smaller regions of space, despite the fact that those regions still span our entire field of view, in all directions of the sky.
In fact, when astronomers map the CMB, they are mapping a sphere that surrounds us and that is very close to that initial moment—at roughly 400,000 years after the big bang—and thus has a “radius” of around 13.7 billion light-years. But its circumference is a lot smaller than what you would expect from Euclidean geometry—more than a thousand times smaller. Spheres that are even closer to the big bang are even smaller, until our field of view converges to that single point we call the big bang. Theoretically, we could cast a laser in any direction and still aim at that single point.
One very bizarre consequence of the non-Euclidean nature of the observable universe is that distant objects appear larger than their true size. For the first 10 billion light years or so, galaxies look smaller if they are farther away, but beyond that distance they instead start taking up a larger and larger field of view in the sky, as if space itself acted like a magnifying lens. In practice, the effect is exceedingly difficult to actually observe in our telescopes, because at those distances galaxies look extremely faint. But in recent years astronomers have begun several projects to detect the magnification effect in their observations, not by looking at the apparent size of galaxies but at their spacing. To do so, they map hundreds of thousands of galaxies over a range of distances spanning many billions of light-years. “You look at where the galaxies formed, not at how big they are,” explains astronomer Tamara Davis of the University of Queensland, who participates in one such mapping effort called WiggleZ.
Of course, Dante lived five centuries before any mathematicians ever dreamed of notions of curved geometries. We may never know if his strange spheres were a mathematical premonition or esoteric symbolism or simply a colorful literary device.
Editor's picks for further reading
Non-Euclidean Geometry Online: a Guide to Resources
Mircea Pitici's brief introduction to non-Euclidean geometry.
The Poetry of the Universe
Mathematician Robert Osserman's volume of "math for poets."
The World of Dante
Explore Dante's writing with interactive maps, images, music, and more.
The universe is simple.
Simulation of the sky as viewed by the Bell Labs microwave receiver. Credit: NASA / WMAP Science Team
This is the cosmic background radiation as detected with a Bell Labs radio telescope in 1964. The band across the middle is the center of our galaxy. The rest is the humming echo of the Big Bang, uniform in every direction—just as theorists had been predicting.
“Which is an amazing thing,” P. James E. Peebles—one of the very same cosmologists who helped predict it—recalls thinking. “But there it is: The universe is simple.”
As Einstein once famously said, “The most incomprehensible thing about the universe is that it is comprehensible.” But why should it be? Why would something so vast and complex and old be within the comprehension of a species that spent millennia believing it occupied the center of existence? Yet century after century cosmologists have operated under the assumption that the universe is simple, and it appears to have worked—at least so far.
That assumption goes back to Copernicus. The picture of the heavens he inherited from the ancients was crowded with invisible spheres that carried the moon, sun, planets, and stars. The geometry to explain those motions was embroidered with epicycles and deferents—circles, and circles within circles, and circles adjacent to circles, all fabricated by astronomers over the course of a couple of millennia in an attempt to make sense of the motions of the celestial bodies around a stationary Earth. The problem with this picture, Copernicus realized, was that it divided the universe into two realms, the terrestrial and the celestial. What if the universe instead was one big happy realm? Once Copernicus removed the Earth from its place of privilege and set it in orbit around the sun, he arrived at equations that predicted the motions of the heavens with far greater accuracy. A century and a half later, Isaac Newton used the sun-centered model to create his law of universal gravitation—emphasis on “universal.” By uniting the physics of the terrestrial with the physics of the celestial, he showed that Copernicus was right: The universe is simple.
For the next three centuries, the discoveries of moons and planets and comets corroborated Newton’s idea, with one exception: an aberration in the orbit of Mercury. In 1915 Einstein fixed that problem, via the general theory of relativity, by reconceiving gravity not as a force that acts across space but as a property of space itself. Two years later, he published a paper exploring the “cosmological considerations” of this new view of gravity. What might this tweaked law of universal gravitation have to say about the history and structure of the universe? To keep the math simple, Einstein and then other theorists had to assume the universe was simple, too. So they returned to Copernicus’s assumption: The Earth doesn’t have a privileged position in the universe. On the largest scale, the cosmos would look the same in every direction no matter where you are in it.
Which was what the 1964 vision of the cosmic background radiation revealed. This picture of the universe, however, was almost too simple. Where were the subtle fluctuations in temperature that would represent the seeds of the galaxies, clusters of galaxies, and superclusters of galaxies—everything that would grow into the universe as we know it?
To answer that question, NASA set to work designing a satellite to look for those fluctuations. In 1991 and 1992, that satellite, the Cosmic Background Explorer (COBE), found them—differences in the temperature at a level of one part in 100,000:
The sky as seen by COBE. Credit: NASA Legacy Archive for Microwave Background Data Analysis (LAMBDA)
I met the the co-principal investigator of that project, George Smoot, in his office at the University of California, Berkeley, just days after he won the Nobel Prize in physics. Never a particularly calm presence, he was even more animated on this occasion. Underslept and overadrenalized, he shouted, “Time and time again the universe has turned out to be really simple!”
Sitting across from him, nodding emphatically, was fellow physicist Saul Perlmutter of Lawrence Berkeley National Laboratory. “It’s like, why are we able to understand the universe at our level?” he said, echoing Einstein.
Yet Perlmutter himself is among the scientists whose work has most threatened the notion that the universe will be ultimately comprehensible. In 1998, he was the leader of one of the two teams that found the expansion of the universe is not slowing down, as you might naively expect, but speeding up. (He would share the Nobel for that discovery in 2011.) At first physicists considered the discovery of “dark energy” difficult to accept—a force more powerful than gravity on a cosmic scale?—but in 2003 came the first results from the successor to COBE, the Wilkinson Microwave Anistropy Probe (WMAP):
The sky as seen by WMAP. Credit: WMAP Science Team, NASA
By reading the patterns in those even finer fluctuations, cosmologists could calculate the portion of the universe that takes the form of dark energy: 72.8 percent. So what is it?
Yet before theorists can begin to answer that question, they need to know how dark energy behaves. Does it vary across space and over time, or is it constant? The successor to WMAP, the Planck satellite, should provide a strong clue when its results are released early next year. So far, though, all the data from less precise experiments are pointing toward dark energy being constant. In that case, theorists agree, the answer to “What is dark energy?” will require them to unite the physics of the very big (relativity) with the physics of the very small (quantum mechanics), just as Newton had united the physics of the terrestrial with the physics of the celestial.
“We shouldn’t be shocked that we’re finding a few surprises,” Perlmutter later told me. “Based on just some fragment of information, and a very interesting theory of Einstein’s, people were able to try out the simplest possible model of the universe. ‘We don’t know anything but let’s imagine that it’s as simple as it could possibly be, because we have no other information to go on.’ And then they said, ‘Let’s take a few more pieces of information,’ and those pieces of information fit, and they fit well into this ridiculously simple, intentionally cartoonish picture.”
But now? We don’t know what the vast majority of the universe is. And, physicists acknowledge, we might never know. The universe just might be incomprehensible after all. But assuming the solution exists, Perlmutter at least has faith as to what it will look like: Copernicus’ solution, and Newton’s, and Einstein’s.
“Something,” he said, “equally elegantly simple.”