Thursday, July 26, 2012

You Don't Have to Blow Up the Universe to Be Cool

This was supposed to be a story about dark energy. It still is -- dark energy is one of the most intriguing mysteries in cosmology, after all -- but it's mostly a story about cosmic doom, why I love theoretical physics, and why you shouldn't believe everything you read on io9.

What goes up...

It's difficult to express to a non-physicist just how weird dark energy is, because most people are used to encountering things that they don't understand in physics, and they generally assume that someone else is on top of the situation. That's not the case with dark energy. Here's an analogy. Let's say you're throwing a ball in the air. There are logically two possibilities: (1) You throw it, it goes up for a while, slows down, and falls back to Earth. (2) If you happen to have superhuman strength, you throw it hard enough that it escapes Earth's atmosphere and then sort of coasts forever through the void. But imagine neither of those things happen. Imagine instead that you toss the ball up in the normal way, and it looks like it's starting to slow down, but just as you think it's about to reach its maximum height and come back, it suddenly speeds up and shoots off into space.

That's not supposed to happen.
[Source: Norwalk Citizen Online, Christian Abraham / Connecticut Post. ]
Dark energy is like that. It's actually the exact same physics. The big bang is like the throw, starting off the expansion of the Universe. That expansion means distant galaxies are all moving away from us, but since all those galaxies have mass and gravity is still always attractive, ultimately everything in the Universe should be pulling on everything else. This should slow the expansion down, through the same kind of attraction that pulls the ball toward the Earth, slowing it down and keeping it from floating away. But a couple decades ago astronomers discovered that the expansion isn't slowing down at all. There's something out there in the cosmos that's acting against the gravity of all those galaxies. It's not just keeping the Universe from recollapsing, it's actually pushing all the galaxies apart faster and faster, accelerating the expansion. And just as physicists would be at a loss to explain why your baseball suddenly went (non-)ballistic, everything we understand about physics tells us this should not be happening to the Universe. We call it dark energy because we have no idea what it is.

The cosmological constant

We have some theories, of course. In fact, there are probably hundreds of theories, many of them difficult to distinguish from one another with the data we currently have. The most familiar and longest-standing idea is that of the cosmological constant -- a sort of fudge factor that Einstein originally put into his equations of gravity. He wasn't trying to explain acceleration -- at the time, he thought the Universe was static, and he needed an anti-gravity term to balance out the pull of all the mass in the Universe. He discarded the extra term in embarrassment when the expansion of the Universe was discovered, but this new acceleration is making many cosmologists now think we need to put it back in.
The equation governing the acceleration of the expansion of the Universe, with a cosmological constant term. The gravity term includes the density (p) and pressure (ρ) of all matter and energy -- the minus sign means this term slows the expansion. The cosmological constant term (with Λ) has a positive sign, and therefore contributes to acceleration. The parameter a is the scale factor measuring the size of the Universe, and the double dots indicate the second derivative (acceleration) with respect to time. 
A definining property of the cosmological constant is, unsurprisingly, that it is constant. In fact -- and this is almost weirder than the acceleration -- the density of the "stuff" described by the cosmological constant stays the same even as the Universe expands. If you have a box filled with cosmological constant, and you suddenly make the box twice as large without opening it or putting anything in, you now have twice as much cosmological constant in your box. As I said: it's weird.

The cosmological non-constant?

Unfortunately, the cosmological constant isn't really that appealing a solution, since it still looks a lot like a fudge factor and it seems somewhat arbitrary. The main alternative is dynamical dark energy, which is any kind of dark energy that can change with time. Most theories of dynamical dark energy (often just called "dark energy" as opposed to a cosmological constant, which is sort of a special case) involve scalar fields. Until recently, we had no evidence whatsoever for scalar fields in nature, even though they were constantly popping up in theories. Now that we think we might have discovered the Higgs boson (yay!), we have evidence for the first scalar field: the Higgs field. The Higgs field itself doesn't have anything to do with dark energy, but it's comforting that at least one example of a scalar field might actually exist. The nice thing about a scalar field is that it can have the same value everywhere in space while varying with time, which is just what you need if you want some kind of time-dependent dark energy that fills the Universe.

So how do we distinguish between a cosmological constant and dynamical dark energy? The usual way is to look at the relationship between the dark energy's pressure (denoted p) and density (denoted, somewhat confusingly, by the Greek letter rho: ρ). One of the key features of any form of dark energy is the fact that it has negative pressure.

In general relativity, pressure is a form of energy, and energy has a gravitational effect -- your pressure adds to your gravitational field. (So, gravitationally, pressure pulls.) Negative pressure, therefore, subtracts from a gravitational field, and counteracts gravity -- it pushes. For a cosmological constant, the pressure is exactly -1 times the density: p=-ρ. (I'm using units where the speed of light is 1. You could also write this as p=-ρc2.) For other forms of dark energy, there could be a different relationship.

We use a parameter called the equation of state, w=p/ρto describe the ratio of pressure to density. All substances have one: pressureless matter has w=0; radiation has w=1/3. For a cosmological constant, w=-1.

As far as we can tell from astronomical measurements, w is pretty darn close to -1. Every measurement we've done is consistent with w=-1, and every time we improve on our measurements, we find a value of w even closer to -1. But it would be hard to say for sure that w is exactly -1, because all measurements have uncertainties associated with them. We may at some point measure a value of w that is infinitesimally close to -1, but, without some other reason to believe that we have a cosmological constant, we'll never be able to say that it's not just very slightly higher or lower.

The importance of asking "What if...?"

Until about 10 years ago, no one really talked about the idea that w could be less than -1. Anything with w<-1 was called phantom energy and was considered way too uncouth to be plausible. There are good theoretical reasons for this: constructing a theory with w<-1 is difficult, and if you manage to do it, you've probably had to do something tricky like introduce a negative kinetic energy, which is the sort of thing that would make a ball roll up a hill instead of down. You might even accidentally invent a theory with time travel and wormholes. So it was generally thought that we should leave w<-1 alone, and people made constraint plots like this:
Fraction of the Universe made of matter (Ωm) plotted against the dark energy equation of state parameter (w). Values in the orange region have a good fit to the data. [Source: Caldwell, Kamionkowski & Weinberg 2003 (PRL, 91, 071301)]
This is a plot of the fraction of the Universe made of matter (Ωm) versus w. The colored swaths are where the parameters are allowed by different kinds of observations. The orange is the most favored region. You can see from the plot that everything converges around w=-1: a cosmological constant.

But a group of theorists at Dartmouth and Caltech (Rob Caldwell, Mark Kamionkowski and Nevin Weinberg) looked at that and thought, "Maybe it's not converging at w=-1 -- maybe it just looks that way because it's really converging at some value of w less than -1. What would happen if that were the case?"
Same as above figure, but with the range extended to allow w<-1.
[Source: Caldwell, Kamionkowski & Weinberg 2003 (PRL, 91, 071301)]
And then they wrote my favorite paper ever [Caldwell, Kamionkowski & Weinberg 2003 (PRL, 91, 071301)].

Theory is awesome

It really is an amazing paper. Honestly, you should check it out. I wouldn't ordinarily recommend a theoretical physics paper to a general audience, but this paper is so well written, so accessible, and so beautiful that I can't resist. And it's only 4 pages long.

The authors start from a very simple idea: "What if some day we look at the data and we find out that w<-1?" It doesn't sound like a revolutionary idea, but no one had ever followed that idea to its logical conclusion. So they do it, and after jotting down just a few fairly simple equations, they discover that the universe would rip itself apart.

How often do you get to invent an ultimate cosmic doomsday in the course of your professional life? This is the kind of work I got into theoretical physics to do. It's awesome.

Here's how it works. I said before that w=-1 is a cosmological constant -- the energy density doesn't increase or decrease as the Universe expands. It turns out that if w>-1, that means that the energy density goes down as the Universe expands (like ordinary matter). Expand a box of matter and you have the same amount of matter, but more space, so your matter is now less dense. But if w<-1, the energy density increases as the Universe expands. Think about that for a minute. If you have a box of phantom energy, and you suddenly make the box twice as big, you now have more than twice as much phantom energy in your box.

Aside from being unsettling, this kind of behavior can actually have some pretty gruesome consequences for the Universe. If we stick with our familiar cosmological constant, then as the Universe expands, even though all the galaxies are moving away from each other, anything that's gravitationally bound stays bound, because there's just not enough dark energy in any bound system (like a solar system or a galaxy) to mess with it. But with phantom energy, the amount of dark energy in any bit of space is increasing all the time, so a planet orbiting a star will actually eventually be pushed away to drift on its own. Everything will become isolated.

And that's not even the worst of it. Caldwell and his colleagues realized that if the density of dark energy is increasing with time, it will eventually be accelerating the expansion of space so quickly that the cosmic scale factor -- the parameter that measures the characteristic size of a region of space -- will reach infinity in a finite time. If the scale factor is infinite, that means that the space in between any two points is infinite, no matter how close they were to begin with. It means that spacetime itself is literally torn apart. When Caldwell and his colleagues realized they'd discovered a new possible end state of the Universe, they dubbed it, appropriately, the big rip.

Animation of the big rip (link to original). From Caldwell, Kamionkowski & Weinberg's paper: It will be necessary to modify the adopted slogan among cosmic futurologists — ‘‘Some say the world will end in fire, Some say in ice’’ — for a new fate may await our world.  [Source: NASA/STScI/G.Bacon]


Having just invented a new cosmic doomsday, the authors decided to go a step further. They worked out exactly when the big rip would occur for any given value of w, and then, for a specific example (w=-1.5, which would have a big rip about 21 billion years from now), they worked out exactly how long we'd have to wait before all of the cosmic structures we know and love be destroyed. Galaxy clusters would be erased 1 billion years before the end. The Milky Way would be dismantled with 60 million years to go. At doom-3 months, the Earth would drift away from the Sun. With 30 minutes to go, our planet would explode, and atoms would be ripped apart in the last 10-19 seconds. Discussing this handy timetable of doom, the authors state with admirable detachment that, were humans to survive long enough to observe the big rip, we might even get to watch the other galaxies get torn apart as we await the end of days. I'm sure that would be lovely.

io9, you have forsaken me

Given my affection for the original phantom energy paper, you can imagine I was intrigued the other day to see an article on the io9 website proclaiming "The Universe Could Tear Itself Apart Sooner Than Anyone Believed." Could it be some new evidence for phantom energy, I thought? Sadly, no. It turned out to be an utterly overblown scare-piece that had hidden all the beauty of the physics behind false assertions and dramatic flaming-Earth graphics.

The io9 post discusses the work of Li and colleagues, researchers in China who have published an article called "Dark Energy and the Fate of the Universe." The paper isn't bad, or even really wrong (though I don't agree with all of it). But it's really nothing new or interesting. It starts from the assumption that dark energy is dynamic and that it is evolving to have w<-1 in the future. It then uses a new parameterization of the evolution of w to draw conclusions about the fate of the Universe.

I won't go into a lot of details, but the gist is as follows. If you want to determine if w is changing with time, you have to start with some model for how it's changing -- basically, you have to assume a functional form. You look at data from the past, determine what w was then, and choose some function for w that changes with time and try to measure its parameters. In cosmology, we usually discuss time in terms of redshift (denoted by z), which is a measure of how much the Universe has expanded since whatever bit of the past we're observing. The redshift z decreases with time and is zero today; future times have negative redshifts.

A typical parameterization of dark energy looks like this: w(z) = w0 + wa (z/(1+z)). The form doesn't matter so much except in that w0 is the value of w today, a positive value of wa means w is decreasing with time, and a negative wa means it's increasing. This parameterization has the property that it goes to infinity in the future at z=-1. Li and colleagues don't like this, but it's hard for me to see why it matters. A redshift of -1 corresponds to an infinite scale factor, which is a big rip. If the only problem with the formula occurs when the big rip is actually in progress, it's hard to see why that should be a big deal for determining anything that happens up to that point.

In any case, they have an alternative, slightly more complicated parameterization, for which w doesn't go to infinity at z=-1: w(z) = w0 + wa [ln(2+z)/(1+z) - ln(2)]. In their formulation, a positive wa means w is increasing, and a negative wa means w is decreasing. They run some simulations and find out that the best-fit points for w0 and wa -- the values the data seem to be pointing to -- imply a big rip will occur.
Constraints on wa and w0 for the model by Li and colleagues. The red point indicates their best fit. The green point is a cosmological constant. The brown region is the best-fit region and the blue region is the 95.4% confidence region. [Source: Li X D et al. 2012 (Sci China-Phys Mech Astron 55,1330)] 
Shouldn't I be scared?

The fact that the best-fit point implies a big rip sounds important, but it isn't really. Many of the latest results have a best-fit value for w that's less than -1; the data just aren't yet good enough for us to draw any conclusions. A cosmological constant easily fits the data, and there's no compelling evidence that dark energy is anything more exotic. Also, as Li and colleagues readily admit, all their conclusions are based on the assumption that dark energy follows their own special functional form -- if it doesn't (and there's no reason to think it would), there's nothing they can say about what would happen.

Nonetheless, Li and colleagues go on to calculate when the big rip would occur with both their best-fit value and their worst-case value (the value still allowed by the data in which the big rip happens soonest) and they say that doomsday could be as soon as 16.7 billion years from now. They even include their own timetable of doom, with earlier times than the original one.

It's a reasonable calculation to make, but I wouldn't call it newsworthy. The comparison they make to say it's "earlier than we thought" is with Caldwell's doomsday value, which used an arbitrarily chosen w=-1.5 for illustrative purposes, not from a fit to any data. The io9 people apparently got hooked by an unreasonably enthusiastic press release and ran with it, trying to stir up the paper's conclusions to make it as significant and alarming as possible.

Disappointingly, the io9 article also contains several blatantly wrong statements, such as "cosmologists are pretty sure dark energy has a value less than -1" (not true!) and "a likely value of -1.5" (completely ruled out!) and "the cosmologists are fairly convinced that w will continue to exhibit a value less than -1 well into the future" (also totally wrong!). Phantom energy is truly an awesome idea, but I don't think many cosmologists would say it's especially likely, and certainly none of us would bet the house. The theoretical problems are substantial and the data just aren't good enough yet for us to say anything either way. The big rip scenario is still fun to think about; it's not necessary to think it's actually imminent to appreciate that. Probably dark energy is a cosmological constant -- and plenty weird enough.

Did I mention theory is awesome?

As a theorist, I encounter a lot of really bizarre ideas. Sometimes I encounter an idea like phantom energy, which is incredibly cool and leads to some truly revolutionary possibilities ... but is probably ultimately wrong. Other times, I get to study something like dark energy, which is mind-bending in a totally different way: not because it breaks physics and makes the Universe blow up, but because it is, contrary to all our understanding, actually out there, just waiting for us to figure it out.