by Katie Mack
The first thing all these possibilities have in common is that they all make sense, physically; they work well with Einstein’s equations of gravity. The other is that for all of them, the present-day expansion is slowing down. At the time the supernova measurements were made, there was no reasonable physical mechanism to make a universe speed up in its expansion. It was just as weird as if you were throwing a ball up into the air and it slowed down a bit and then suddenly shot off into space for no reason. Exactly that weird except for the ENTIRE UNIVERSE.
Figure 10: Open, closed, and flat universes and their evolution over time. The diagrams above indicate the shape of space for three different cosmic models. In an open universe, parallel light beams diverge over time. In a closed universe, they converge. In a flat one, they remain parallel. The different geometries correspond to different fates of the cosmos as shown in the graph. In the closed case, there is enough gravity to cause the cosmos to recollapse, whereas in the open case, the expansion wins out and the universe expands forever. A perfectly balanced flat universe continues expanding but always slowing in its expansion rate. However, if a universe contains dark energy, its expansion can accelerate (while the geometry of space remains flat).
The measurements were checked, and rechecked, but they kept forcing physicists to the same conclusion. The expansion was accelerating.
These were desperate times, and they called for desperate measures. So desperate, in fact, that the astronomers invoked the existence of a vast cosmic energy field that could make the empty vacuum of space itself have an intrinsic outward push in all directions—a previously undetected property of spacetime that would make the universe expand forever, all on its own, from an ever-present energy source, never depleting. A cosmological constant.
NOT-SO-EMPTY SPACE
Unlike most monumental revisions of the foundations of physics, the cosmological constant was not a new idea at all. It was, in fact, originally Einstein’s brainchild,II and it fit nicely into his equations of gravity governing the evolution of the universe. But it was based on a deeply mistaken notion, and by rights it should never have been written down in the first place.
Einstein’s heart was in the right place. The purpose of the cosmological constant was to save the universe from catastrophic collapse. Or more accurately, from having catastrophically collapsed already. Being an expert, as he was, in all things gravitational, Einstein knew that all the data available pointed to the uncomfortable conclusion that gravity should have destroyed the universe long ago. This was 1917, half a century before widespread acceptance of the Big Bang theory, when the cosmos was still largely thought to be static and unchanging. Stars could live and die, matter might slightly rearrange, but space was space—it was just a background on which other things happened. So when Einstein saw that there were stars in the night sky, apparently stationary, he knew the universe was in trouble. Every one of those stars, he figured, should be gravitationally attracting every other star, and slowly drawing together over time. It doesn’t help for the other stars to be really distant, either; gravity is an infinite and purely attractive force. (It should be noted that this was a time before it was clear that other galaxies existed, or he would have applied the argument to galaxies instead. The problem would be the same.) In an unchanging universe, you can never be far enough away from something to not feel its pull, at some level, and that pull should be bringing you together over time. Einstein’s own calculations said that any universe populated with massive objects should already have collapsed upon itself. The very existence of the cosmos was a contradiction.
This, of course, looked bad. Fortunately, Einstein found room in his General Theory of Relativity to add a little universe-rescuing tweak. Nothing in space could counter the gravity of the stars, but perhaps space itself could do it. Einstein had already developed a beautiful equation to describe how the shape of space responded to the gravitational attraction of all the stuff in the cosmos. All he had to do to ensure gravitational attraction wouldn’t immediately collapse space was to decide his equation was incomplete, and to tack on a term that could stretch out the space between gravitating objects, perfectly balancing the contraction that gravity would otherwise cause. The term didn’t represent a new component of the universe, but a property of space itself, where each piece of space has a kind of repulsive energy to it. When you have a lot of space and not much matter (like in the space between stars or galaxies), that repulsive energy can counter gravitational attraction.
Success! The equation worked. It nicely described a static universe in which the existence of other stars or galaxies doesn’t immediately collapse the entire cosmos. Einstein had done it again.
Only problem: the universe is not static. This became apparent to the astronomical community a few years later, when it turned out that fuzzy smudges in the sky previously called “spiral nebulae” were actually other galaxies. Soon after, Hubble used the redshifting of those galaxies to show the universe was actually expanding. While a static universe with only attractive gravity is doomed, an expanding universe can be saved, at least temporarily, by its own expansion. The gravity might slow the expansion, and might eventually turn it around, but a universe can get along just fine for many billions of years on an initial growth spurt and the ongoing effects of that expansion. (How the expansion started is a whole other story, but all we need for this particular problem is for the universe to not be so profoundly doomed that it would already be toast, and either a cosmological constant or expansion can take care of that.)
The discovery of the expanding universe meant a whole new view of cosmology and a minor embarrassment for Einstein. He somewhat reluctantly removed the cosmological constant term from his equations and wandered off to try to revolutionize some other area of fundamental physics. And so things went, with the evolution of the universe making a reasonable amount of sense, right up until the supernova measurements made a mess of it all again in 1998. Accelerated expansion meant the cosmological constant had to be revived, with the only small mercy being that it was by then far too late for Einstein to say, “I told you so.”
Just because a cosmological constant allows the universe to be accelerating in its expansion doesn’t mean it’s broadly considered to be a good and sensible solution.III There’s nothing that explains why the cosmological constant term should have the value it does, from a theoretical standpoint. Why should it exist at all, except as a suspiciously convenient fix to our equations? And if we have to have a cosmological constant, why not a larger value? One of the most logically natural ways for the universe to have a cosmological constant would be for the constant to derive from the vacuum energy of the universe—the energy of empty space that accounts for weird things like virtual particles that can quantum-fluctuate in and out of existence. But calculations of the vacuum energy required for quantum field theory give us a number 120 orders of magnitude larger than what the cosmological constant actually out there in space seems to be. In case you’re not familiar with the term, an order of magnitude is a factor of 10. 100 is two orders of magnitude. 120 orders of magnitude is 10 raised to the power of 120. Even in astrophysics, where we sometimes play fast and loose with the numbers, this looks like a major discrepancy. So, if the cosmological constant isn’t the vacuum energy quantum field theorists all know and love, what is it?
One suggested solution to this “cosmological constant problem” involves the hypothesis that the constant is small in our observable universe, but might take other values far away, and it’s just a matter of chance that we are where we are. (Or, not chance, but necessity, if vastly different values of the cosmological constant would be hostile in some way to the development of life and intelligence, perhaps by making space expand too fast for galaxies to form.) Another possibility is that it’s not a cosmological constant at all, but some kind of new cosmological-constant-mimicking energy field in the universe that might change over time, in which case there’s a possibility that it evolved to what it is for
some other reason.
Because we don’t know whether it’s really a cosmological constant or not, we generally call any hypothesized phenomenon that could make the universe accelerate in its expansion dark energy. To throw some more terminology into the mix, an evolving (i.e., nonconstant) dark energy is often called quintessence, after the “fifth element,” a mysterious something-or-other that was popular to philosophize about in the Middle Ages and is not really much more precisely specified now. A nice thing about the quintessence hypothesis is that it could lead us to a theory with some parallels to the cosmic inflation at the beginning of time. We know that whatever it was that caused cosmic inflation eventually turned off, so perhaps a similar accelerated-expansion-causing field could have turned on since then, causing the acceleration we see today.
(One downside of the quintessence hypothesis is that it’s theoretically possible for a dark energy that changes over time to violently destroy the universe. For instance, if whatever is accelerating the expansion now turns around, it could cause the universe to stop and recollapse, bringing us back to a Big Crunch after all. Fortunately, that looks very unlikely, though we can’t entirely rule it out.)
In any case, based on observations at the moment, it really looks a lot like dark energy is a cosmological constant: an unchanging property of spacetime that has only recently (i.e., in the last few billion years) come to dominate the evolution of the universe. At early times, when the cosmos was more compact, there just wasn’t enough space for the cosmological constant (which is a property of empty space) to do very much, so the expansion at that time was slowing down, just as we would have expected. But about five billion years ago, matter got so diffuse due to ordinary cosmic expansion that the inherent cosmological-constant-induced stretchiness of space started to really become noticeable. We can now measure the motion of supernova explosions so far away that they went off before the expansion started to speed up, meaning that we can trace out when the universe was decelerating, and pretty much exactly when it transitioned to acceleration. Dark energy still might be some new, dynamical field. But so far, a cosmological constant fits the data perfectly.
If we follow that through to its future consequences, it’s kind of ironic, actually. Because now it seems that the term Einstein used to save the universe will end up spelling its doom.
THE INFINITE COSMIC TREADMILL
A cosmological-constant-induced apocalypse is a slow and agonizing one, marked by increasing isolation, inexorable decay, and an eons-long fade into darkness. In some sense, it doesn’t end the universe exactly, but rather ends everything in it, and renders it null and void.
The reason a cosmological constant dooms the universe is that once it starts, the accelerated expansion never, ever stops.
* * *
The present-day observable universe is probably bigger than you think. The “observable” part refers to the region within our particle horizon. We define this as being the farthest we could possibly see, given the limitations of the speed of light and the age of the universe. Since light takes time to travel, and more distant objects are, from our perspective, farther in the past, there has to be a distance corresponding to the beginning of time itself. A distance at which, if a light beam started there at the first moment, it would take the entire age of the universe to reach us. This defines the particle horizon, and it’s the farthest out we can observe anything at all, even in principle. Knowing that the universe is about 13.8 billion years old, logic would tell you that the particle horizon must be a sphere of radius 13.8 billion light-years. But that’s assuming a static universe. In actual fact, since the universe has been expanding all that time, something just close enough to send its light to us 13.8 billion years ago is now much farther away—approximately 45 billion light-years. So we can define the observable universe to be a sphere of about 45 billion light-years in radius, centered on us.IV
The closest we can get to seeing that “edge” is the cosmic microwave background, whose light comes from almost as far as the particle horizon. But a bit closer to us, we can also see ancient galaxies that are now more than 30 billion light-years away. The light we see from those galaxies started traveling through the universe long before they got to such incredible distances, though. If not, we wouldn’t be able to see them at all, since the light coming from them nowV can’t ever reach us. It turns out that in a uniformly expanding universe, where the more distant things are receding more quickly, it is inevitable that there is a distance beyond which the apparent recession speed is faster than the speed of light, so light can’t catch up.
“Wait!” you might be saying. “Nothing can travel faster than light!” This is a fair point, but it doesn’t actually lead to a contradiction. While nothing can travel faster than light through space, there’s no rule that limits how quickly things can happen to find themselves farther apart because they are sitting still in a space that’s getting bigger between them.
The distance at which galaxies are currently moving away from us faster than light is surprisingly close, given how far we can actually see. We call it the Hubble radius, and it’s around 14 billion light-years from here. I mentioned in Chapter 3 that we can label the distance to objects by their redshift factors—the amount that their light is shifted toward the red (low frequency/long wavelength) part of the spectrum due to the expansion of the universe. An object at the Hubble radius would have a redshift of about 1.5, meaning the light wave, and the universe itself, has stretched out to two and a half times its original length since the light was emitted.VI But even that utterly unimaginable distance is, in cosmological terms, just around the corner. We’ve seen individual supernovae out to redshifts of almost 4. The most distant galaxies we’ve seen have been at redshift values of about 11, and the cosmic microwave background is at a redshift of around 1,100.
So how do we see so many things that are so far away that they’re receding from us at more than the speed of light, and, in fact, always have been? If something is moving away at more than the speed of light, a light beam emitted from it is getting farther away from us, not closer. The trick is that the light we’re picking up left the source long ago, when the universe was smaller and the expansion was actually slowing. So a light beam that started out being carried by the expansion of space away from us (even though it was emitted in our direction) eventually was able to “catch up” as the expansion slowed and it reached a part of the universe that was close enough for the recession speed to be less than the speed of light. It entered our Hubble radius from the outside.
Imagine you’re standing in the middle of a very long treadmill that’s going faster than you can run. Even running at your top speed, you’re going to be dropping back. But if you don’t get dragged back too far, and if the treadmill slows down enough, you can eventually make up the lost ground and start to move forward before falling off the back end. So if you’re in a universe whose expansion is slowing down, you’ll be able to see more and more distant objects as time goes on, as the light from distant objects catches up with the expansion. The “safe zone” in which the expansion speed is less than the speed of light, the Hubble radius, grows over time and envelops objects that were previously outside it. Our horizons,VII so to speak, expand.
Figure 11: The Hubble radius now and in the future. As the expansion of the universe accelerates, galaxies that are currently inside our Hubble radius will be outside it. Eventually, no galaxies outside our Local Group will be visible.
Dark energy ruins everything, though. Because of dark energy, the expansion isn’t slowing anymore—in fact, it has been speeding up for about the last five billion years. And while the Hubble radius is still technically growing in physical size, it’s growing so slowly that the expansion is pulling previously visible objects outside it. We can see extremely distant objects whose light crossed into our Hubble radius before the acceleration began, but anything whose light isn’t in the safe zone now will remain invisible forever. (More on that later.)
Even without the dark energy complication, an expanding universe can be a hard thing to wrap your head around.VIII
The fact that the universe is expanding means it was smaller in the past: fine.
The fact that it was smaller in the past means that something that is far away now was closer in the past: okay.
That, in turn, means that there’s a very distant galaxy we can currently see that was, billions of years ago, kind of nearby: right.
And long ago that galaxy shot out a beam of light that was originally moving directly away from us despite being pointed in our direction, but which from our perspective then sort of stopped and turned around and has just now arrived: sure, from a certain point of view, that might make sense.
BUT IT GETS EVEN STRANGER.
I’m sorry for shouting. I really am. But I’m not going to sugarcoat this. The universe is frickin’ weird and this whole Hubble-radius-observable-universe thing is a big part of that and it makes deeply bizarre things happen. And now I’m going to tell you one of the most mind-blowing bits of weirdness I know about cosmology. You know how when something is far away, it looks smaller? This is a totally normal thing. The farther away something is, the smaller it looks. People look tiny from airplanes. Distant buildings can be covered with your thumb. Everyone knows that.
Except out there in the universe? Not so much.
