by Katie Mack
This is reassuring. If you happen to be a clump of matter in the universe, and you would like to form a nice stable gravitationally bound galaxy, you can rest assured that once you get enough matter together to build something, dark energy won’t ruin all that hard work.
Unless, that is, the dark energy is something more powerful than a cosmological constant.
As we discussed in the previous chapter, a cosmological constant is just one possibility for dark energy. All we really know about dark energy is that it’s something that makes the universe expand faster. Or, more precisely, it has negative pressure. Negative pressure is a weird concept, because normally one thinks of pressure as something that pushes outward. But in Einstein’s general-relativistic way of thinking about the universe, pressure is just another kind of energy, like mass, or radiation, and is thus gravitationally attractive. And in general relativity, gravitational attraction is just a consequence of the bending of space.
Remember the picture of the bowling ball creating a dent in the trampoline as an analogy for the effect of matter on the curvature of space? If you take general relativity into account, the dent is deeper if the ball is more massive, but also if it is hot, or if it has high internal pressure. So pressure, like other forms of energy, acts a lot like mass. From a gravitational perspective, pressure pulls. When you calculate the gravitational effect of a clump of gas, for instance, you have to factor in not just its mass, but its pressure, and both contribute to the gravitational impact that gas has on the stuff around it. In fact, the pressure contributes more to the spacetime curvature than the mass does.
What does that mean for something with negative pressure? If the pressure of some weird substance can be negative, it means that it can effectively cancel out the mass of the stuff, at least as regards its impact on the curving of spacetime. If you write down the pressure and density of dark energy in the form of a cosmological constant, in the appropriate units, the pressure is exactly the negative of the density.
We usually talk about the relationship between a substance’s density and its pressure using a number called the equation of state parameter, written as w—it’s equal to pressure divided by energy density, in units in which that comparison makes sense. Here, we’re interested in the equation of state of dark energy, which, given enough time, will be the equation of state of the whole universe, since dark energy becomes more and more important in the expanding universe as everything else dilutes away. If the measured value of w = -1 exactly, that tells you that the pressure and the density are exactly opposite, and dark energy is a cosmological constant. Since the energy density in a cosmological constant is always positive, at first glance it seems as though it should act just like matter and amp up the gravity that slows down the expansion of the universe. But because the negative pressure is given a heavier weight in the equations, all a cosmological constant ends up doing is contributing toward accelerating cosmic expansion.
At least it does so in a predictable way. A cosmological constant, with w = -1, has a total energy density that is exactly constant over time as the universe expands, without increasing or decreasing. For dark energy with any other value of w, this is no longer the case. So it’s important to figure out what we’re really dealing with here.
In the years after dark energy was first discovered, it was clear that something was making the expansion of the universe accelerate, which meant there had to be something out there with negative pressure. It turns out that anything that has a value of w less than -1/3 gives you both negative pressure and accelerated expansion. But knowing the value of w could tell us whether dark energy is a true cosmological constant (w = -1 always), or some kind of dynamical dark energy whose influence on the universe might change over time. So astronomers went looking for a way to determine the value of w exactly. If dark energy turned out not to be a cosmological constant, this would indicate that we had not only discovered a new kind of physics acting on the universe, but one with the added bonus of being something even Einstein hadn’t foreseen.I
For a few years, this was the name of the game: measure w, find out what’s going on with dark energy. Measurements were made, papers were written, plots were drawn showing which values of w agreed with the data. The cosmological constant case looked like it just might win out.
But in the late 1990s and early 2000s, a small group of cosmologists pointed out a major undiscussed assumption their colleagues were putting into their calculations. It was a perfectly reasonable assumption to make, because neglecting it would violate certain long-held principles of theoretical physics so fundamental that no one wanted to upset them. But these principles weren’t required by the data, and in the end, as scientists, our first loyalty has to be to the data. Even if it means rewriting the fate of the universe.
OFF THE EDGE OF THE MAP
The simple question physicist Robert Caldwell and his colleagues asked was: what if w is less than -1? Say, -1.5? Or -2? Up until this point, such a possibility was generally thought too outlandish to be considered. Plots in papers showing the “allowed” region for w based on the data tended to abruptly cut off at -1. The axis might go from -1 to 0, or -1 to 0.5, but -1 was a hard wall, the same way you might put a hard wall at 0 when guessing a person’s height.
Figure 14: Evolution of dark energy in the form of a cosmological constant or in the form of phantom dark energy, compared with matter and radiation. While a cosmological constant keeps a constant density as the universe expands, in the case of phantom dark energy, the density increases.
But when Caldwell looked at the problem, all the observations of w pointed to a value of -1 or something very close to it. Which suggested that there might be values below -1 that were also allowed by the data, if only someone were to check. This hypothetical dark energy with w less than -1 was dubbed by Caldwell “phantom dark energy” and would be deeply inconsistent with the aforementioned Important Theoretical Principles—specifically, the “dominant energy condition,” which says, roughly, that energy can’t flow faster than light.II This seems like a completely sensible condition to place on the universe, but it’s subtly different than the usual statement that light (or any kind of matter) has an ultimate speed limit, and it’s currently less of a proven physical principle than a Very Good Idea. Maybe it’s flexible?
Caldwell and his colleagues went ahead and calculated constraints based on a full range of possibilities for w. Not only did they find that values below -1 were perfectly consistent with the data, they also found, through a simple, straightforward calculation, that if w is even infinitesimally lower than -1, dark energy will tear the entire universe apart, and it will do so in a finite, calculable time.
I just want to pause for a moment to say that this paper, titled “Phantom Energy: Dark Energy with w < -1 Causes a Cosmic Doomsday,” is one of my absolute favorite papers in physics. It’s not often that you get to take some very mild-seeming alteration to the current perspective, shifting a parameter down by a minuscule amount, and find out that this DESTROYS THE ENTIRE UNIVERSE. Not only that, it gives you a way to calculate exactly how the universe will be destroyed, and when, and what it will look like when it all goes down.
Which is as follows.
THE BIG RIP
You can think of it as an unraveling.
The first things to go are the largest, most tenuously bound. Giant clusters of galaxies, in which groups of hundreds or thousands of galaxies flow lazily around each other in long intertwined paths, begin to find that those paths are growing longer. The wide spaces traversed by the galaxies over millions or billions of years widen even more, causing the galaxies at the fringes to slowly drift away into the growing cosmic voids. Soon, even the densest galaxy clusters find themselves inexorably dissipated, their component galaxies no longer feeling any central pull.
From a vantage point within our own galaxy, the loss of the clusters should be the first ominous sign that the Big Rip is in progress. But the speed of light delays this clue until
we are already feeling the effects much closer to home. As our local cluster, Virgo, begins to dissipate, its previously languid motion away from the Milky Way begins to pick up speed. This effect is subtle, though. The next one is not.
We already have astronomical all-sky surveys that are capable of measuring the positions and motions of billions of stars within our own galaxy.III As the Big Rip approaches, we start to notice that the stars on the edges of the galaxy are not coming around in their expected orbits, but instead drifting away like guests at a party at the end of the evening. Soon after, our night sky begins to darken, as the great Milky Way swath across the sky fades. The galaxy is evaporating.
From this point, the destruction picks up its pace. We begin to find that the orbits of the planets are not what they should be, but are instead slowly spiraling outward. Just months before the end, after we’ve lost the outer planets to the great and growing blackness, the Earth drifts away from the Sun, and the Moon from the Earth. We too enter the darkness, alone.
The calm of this new solitude doesn’t last.
At this point, any structure still intact is straining under the push of the expanding space within it. The Earth’s atmosphere thins, from the top. Tectonic motions within the Earth respond chaotically to the shifting gravitational forces. With only hours to go, the Earth cannot hold together: our planet explodes.
Even the destruction of Earth, could, in principle, be survivable, if, having interpreted the signs, you have already retreated to some compact space-based capsule.IV But that reprieve is short-lived. Before long, the electromagnetic forces that hold together your atoms and molecules cannot hold up against the ever-expanding space within all matter. In the last tiny fraction of a second, molecules crack open, and any thinking beings still holding on are destroyed, torn atom-from-atom from within.
Beyond that point, there is no possibility of watching the destruction, but it carries on nonetheless. Nuclei themselves, the ultra-dense matter in the centers of atoms, are the next to go. The impossibly dense cores of black holes are eviscerated. And at the final instant, the fabric of space itself is ripped apart.
* * *
Unfortunately, we may never be able to say with certainty that we are safe from a Big Rip. The problem is that the difference between a Heat Death–fated universe and one headed for a Big Rip might literally be unmeasurable. If dark energy is a cosmological constant, the equation of state parameter w equals -1 exactly, and we get a Heat Death. If w is at all lower than -1, even one part in a billion billions, dark energy is phantom dark energy, capable of tearing the universe apart. Because it’s impossible to ever measure anything with complete, uncertainty-free precision, the best we may ever be able to do is say that if the Big Rip does occur, it will be so far in the future that all structure in the cosmos will have decayed already by the time it happens. Because even with phantom dark energy, the closer w gets to -1, the farther into the future the Big Rip is pushed. The last time I calculated the earliest possible Big Rip, based on the 2018 data release from the Planck satellite, I got something in the vicinity of 200 billion years.
Figure 15: Big Rip timeline (based on current worst-case scenario for w), adapted from Caldwell, Kamionkowski, Weinberg, 2003. The time until the Big Rip is at least about 188 billion years. The table indicates other moments of destruction in terms of approximately how long before the Big Rip they would occur.
Phew.
But given the potential consequences, both for the universe and for the structure of physics itself, we in the astronomical community put a pretty high priority on figuring out where we currently sit on the scale from w = -1 to Violent Cosmic Doom.V We can’t measure w directly, but we can determine it indirectly by measuring the past expansion rate of the universe and comparing it to our best theoretical modeling of what different kinds of dark energy would have done. We glossed over this a bit in the previous chapter, but it turns out that even just determining the past expansion rate is far more difficult than it seems like it has any right to be. In principle, there are several ways to get at w, and some of them can be done in subtle ways that don’t require calculating the expansion rate at specific distances. But the most straightforward way to get a handle on dark energy is to figure out our full expansion history. And it turns out all the weirdnesses of cosmology come crashing together if you try to do something as simple as answer the question, “How far away is that galaxy?”
LADDER TO HEAVEN
In order to meaningfully compare the local space-expansion rates at two distant points in the universe, you first have to know exactly how distant each one is. This is no big deal for something on Earth, or even something as close as the Moon, since you can measure the distance by bouncing a laser beam off of it and seeing how long the light takes to come back.VI On those kinds of scales, the universe is pretty reasonable. It acts basically like an unchanging space where the distance from A to B is straightforwardly measurable and makes sense and everything works. When it comes to things outside the Solar System, it gets trickier, both because things that are more distant are harder to measure, and because on larger and larger scales, the expansion starts to change the definition of distance itself.
Astronomers have, over the years, patched together with duct tape and twine a set of overlapping definitions and measurements of distance that build upon one another. As kludgy as it still sometimes seems, it’s the result of decades of innovations in observational astronomy and data analysis, and has given us an intuitive but frustratingly difficult-to-implement strategy known as the distance ladder.
Let’s say you need to measure the length of a large room, and all you have is an ordinary-sized ruler. You could lay the ruler down repeatedly until you cover the length of the room, if you don’t mind crawling around on the floor. Or you could be a bit more creative and measure the length of your stride, then just walk across the room, counting steps. If you chose the steps method, you’re creating a distance ladder: a system of measuring a large distance by calibrating your measurements with something more manageable.
In astronomy, the distance ladder has a series of rungs that allow it to extend out to objects that are billions of light-years away. Within the Solar System, direct laser measurements, orbital scalings, and even eclipses help us gather distance data. Beyond that, the next step is to use parallax. This is a method that takes into account the fact that when you change your vantage point, nearby things seem to shift their positions relative to a fixed background more than distant ones do. It’s the same effect that makes a finger held in front of your face seem to jump back and forth when you close one eye and then the other. If we look at a nearby star in June, and then the same star in December, the fact that the Earth is in a different location in its orbit around the Sun means that the star will appear to have moved slightly with respect to more distant background objects. The closer it is, the bigger the shift. Unfortunately, for anything outside our own galaxy, these apparent motions are too small to be perceived, and we need another method—a way to determine the distance of bright objects just from the properties of their light.
The key to everything from here on out is the concept of a standard candle, which we discussed briefly in the previous chapter. This is a kind of object (such as a star) that has some physical attribute that tells you its brightness. Then, by seeing how bright it looks, you can tell how far away it is. Kind of like having a light bulb with “60 Watts” written on it. You know how bright it should be, but you’ll get less light from it when it’s far away.
Of course, nothing in space has its brightness helpfully stamped on it. But we have something almost as good. The breakthrough discovery that first allowed us to use standard candles in astronomy was due to the astronomer Henrietta Swan Leavitt in the early 1900s.VII Working at Harvard Observatory, she discovered that a certain kind of star known as a “Cepheid variable” brightened and dimmed in a predictable way. A Cepheid that’s intrinsically brighter does slow, gradual pulsations, getting a little b
it brighter and a little bit dimmer over a long period. A Cepheid that’s intrinsically dimmer pulsates more quickly, with wide swings between its brightest and dimmest states.VIII
This discovery was revolutionary, and perhaps one of the most important in the history of astronomy, in that it let us finally measure the scale of the universe around us. It meant that anywhere a Cepheid could be seen, we could get a reliable distance and start to make a usable map. By measuring how quickly a Cepheid pulsed, and how bright it looked from here, Leavitt could tell you with great precision how bright it really was, and thus how distant.
How far does this get us? We can see Cepheid variable stars throughout the Milky Way and in nearby galaxies, so we can use parallax for the nearby ones, carefully calibrate the pulsation relationship, and then use the more distant ones to tell us the distances to other galaxies.