by Max Tegmark
• The missing mass is ghostly, being both invisible and able to pass through us undetected. Its gravitational effects suggest that it consists of two separate substances of opposite character, dubbed dark matter and dark energy: Dark matter clusters, dark energy doesn’t. Dark matter dilutes as it expands, dark energy doesn’t. Dark matter attracts, dark energy repels. Dark matter helps galaxies form, dark energy sabotages.
• Precision cosmology has revealed that simple mathematical laws govern our Universe all the way back to its fiery origins.
• As elegant as it is, the classic Big Bang model fails badly early on, suggesting that to understand our ultimate origins, we need to add another crucial piece to the puzzle.
5
Our Cosmic Origins
In the beginning, the Universe was created. This has made a lot of people very angry and been widely regarded as a bad move.
—Douglas Adams, in The Restaurant at the End of the Universe
Oh, no: he’s falling asleep! It’s 1997, I’m giving a talk at Tufts University, and the legendary Alan Guth has come over from MIT to listen. I’d never met him before, and having such a luminary in the audience made me feel both honored and nervous. Especially nervous. Especially when his head started slumping toward his chest, and his gaze began going blank. In an act of desperation, I tried speaking more enthusiastically and shifting my tone of voice. He jolted back up a few times, but soon my fiasco was complete: he was off in dreamland, and didn’t return until my talk was over. I felt deflated.
Only much later, when we became MIT colleagues, did I realize that Alan falls asleep during all talks (except his own). In fact, my grad student Adrian Liu pointed out that I’ve started doing the same myself. And that I’ve never noticed that he does, too, because we always go in the same order. If Alan, I and Adrian sit next to each other in that order, we’ll infallibly replicate a somnolent version of “the wave” that’s so popular with soccer spectators.
I’ve come to really like Alan, who is as warm as he is smart. Tidiness isn’t his forte, however: the first time I visited his office, I found most of the floor covered with a thick layer of unopened mail. I pulled up a random envelope as an archaeological sample, and found that it was postmarked over a decade earlier. In 2005, he cemented his legacy by winning the prestigious prize for the messiest office in Boston.
What’s Wrong with Our Big Bang?
But this prize isn’t Alan’s only achievement. Back around 1980, he learned from the physicist Bob Dicke that there are serious problems with the earliest stages of Alexander Friedmann’s version of the Big Bang model, and proposed a radical solution that he called inflation.1 As we’ve seen in the last two chapters, extrapolating Friedmann’s expanding-universe equations backward in time was extremely successful, accurately explaining why distant galaxies are flying away from us, why the cosmic microwave–background radiation exists, how our lightest atoms originated, and many other observed phenomena.
Figure 5.1: Andrei Linde (left) and Alan Guth (right) at a Swedish crayfish party, blissfully unaware that I’m photographing them, and that they’ll need to dress differently to collect the prestigious Gruber and Milner prizes, which recognize them as the two main architects of inflation.
Let’s go back in time to near the frontier of our knowledge, to an instant when our Universe was expanding so fast that it would double its size during the next second. Friedmann’s equations tell us that before this event, our Universe was even denser and hotter, without limit. That, in particular, there was a beginning of sorts one third of a second earlier, when the density of our Universe was infinite, and everything was flying away from everything else with infinite speed.
Following in Dicke’s footsteps, Alan Guth carefully analyzed this story of our ultimate origins, and realized that it seemed awfully contrived. For example, it gives the following answers to four of our cosmic questions from the beginning of Chapter 2:
Q: What caused our Big Bang?
A: There’s no explanation—the equations simply assume it happened.
Q: Did our Big Bang happen at a single point?
A: No.
Q: Where in space did our Big Bang explosion happen?
A: It happened everywhere, at an infinite number of points, all at once.
Q: How could an infinite space get created in a finite time?
A: There’s no explanation—the equations simply assume that as soon as there was any space at all, it was infinite in size.
Do you feel that these answers settle the matter, elegantly laying all your Big Bang questions to rest? If not, then you’re in good company! In fact, as we’ll see, there’s even more that Friedmann’s Big Bang model fails to explain.
* * *
1Few important scientific discoveries are made by one person alone, and the discovery and development of inflation is no exception, with important contributions by Alan Guth, Andrei Linde, Alexei Starobinsky, Katsuhiko Sato, Paul Steinhardt, Andy Albrecht, Viatcheslav Mukhanov, Gennady Chibisov, Stephen Hawking, So-Young Pi, James Bardeen, Michael Turner, Alex Vilenkin and others. You’ll find interesting historical chronicles of this in many of the books on inflation in the “Suggestions for Further Reading” section at the end of this book.
The Horizon Problem
Let’s analyze more carefully the third question from our list above. Figure 5.2 illustrates the fact that the temperature of the cosmic microwave–background radiation is almost identical (agreeing to about five decimal places) in different directions in the sky. If our Big Bang explosion had happened significantly earlier in some regions than in others, then different regions would have had different amounts of time to expand and cool, and the temperature in our observed cosmic microwave–background maps would vary from place to place not by 0.002% but by closer to 100%.
Figure 5.2: Whereas the molecules of hot coffee and cold milk have ample time to interact with each other and reach the same temperature, the plasma in regions A and B have never had time to interact at all: even information traveling at the speed of light couldn’t have made it from A to B yet, since light from A is only reaching us coffee drinkers at the halfway point today. The fact that the plasma at A and B nonetheless have the same temperature is therefore an unexplained mystery in Friedmann’s Big Bang model.
But couldn’t some physical process have made the temperatures equal long after the Big Bang? After all, if you pour cold milk into hot coffee as illustrated in Figure 5.2, you won’t be surprised if everything mixes to a uniform lukewarm temperature before you drink it. The catch is that this mixing process takes time: you need to wait long enough for milk and coffee molecules to move through the liquid and mix. In contrast, the distant parts of our Universe that we can see haven’t had time for such mixing (Charles Misner and others first pointed this out back in the sixties). As illustrated in Figure 5.2, the regions A and B that we see in opposite directions of the sky haven’t had time to interact at all: even information traveling at the speed of light couldn’t have made it from A to B yet, since light from A is only now reaching the halfway point (where we’re located). This means that Friedmann’s Big Bang model offers no explanation whatsoever for why A and B have the same temperature. So regions A and B seem to have had the same amount of time to cool since our Big Bang, which must mean that they independently underwent a Big Bang explosion at almost exactly the same time, without any common cause.
To better understand Alan Guth’s puzzlement over this, imagine how you’d feel if you checked your email and found a lunch invitation from a friend. And then realized that every other friend of yours has also sent you a separate email inviting you for lunch. And that every single one of these emails was sent to you at the exact same time. You’d probably conclude that this was some sort of conspiracy, and that all the emails had a common cause. Perhaps your friends had communicated among themselves and decided to throw you a surprise party, say. But to complete the analogy with Alan’s Big Bang puzzle, where the regions A, B, et
c., correspond to your friends, imagine that you know for a fact that your friends have never met, have never communicated with each other, and have never had access to any common information before they sent you their emails. Then your only explanation would be that it was all a crazy fluke coincidence. Too crazy to be plausible, in fact, so you’d probably conclude that you’d made an incorrect assumption somewhere, and that your friends had somehow managed to communicate after all. This is exactly what Alan concluded: it couldn’t just have been a crazy fluke coincidence that infinitely many separate regions of space underwent Big Bang explosions all at once—some physical mechanism must have caused both the exploding and the synchronizing. One unexplained Big Bang is bad enough; an infinite number of unexplained Big Bangs in perfect synchronization strains credulity.
This is known as the horizon problem, because it involves what we see on our cosmic horizon, in the most distant regions we can observe. As if this weren’t bad enough, Bob Dicke had told Alan of a second problem for Friedmann’s Big Bang that he called the flatness problem.
The Flatness Problem
As we saw in the last chapter, we’ve measured our space to be flat to high accuracy. Dicke argued that this is puzzling if Friedmann’s Big Bang model is correct, since it’s a highly unstable situation, and we shouldn’t expect unstable situations to last for long. For example, we discussed in Chapter 3 how a stopped bike is unstable, because any slight departure from perfect balance gets amplified by gravity, so you’d be very puzzled if you saw an unsupported stopped bike remain upright for minutes on end. Figure 5.3 shows three solutions to Friedmann’s equation, illustrating the cosmic instability. The middle curve corresponds to a flat universe, which remains perfectly flat and expands forever. The other two curves start out virtually identically on the left side, with space having almost no curvature at all, and after a billionth of a second, their densities differ only in the last of the twenty-four digits.1 But gravity amplifies these tiny differences, and over the next 500 million years, this causes our Universe described by the bottom curve to stop expanding and recollapse in a cataclysmic Big Crunch, a sort of Big Bang in reverse. In this ultimately collapsing universe, space gets curved so that triangle angles add up to much more than 180 degrees. In contrast, the top curve describes a universe getting curved so that these angles add up to much less than 180 degrees. It expands much faster than the flat borderline universe, and by the present day, its gas would be way too diluted to form galaxies, rendering its fate a cold and dark “Big Chill.”
So why is our Universe so flat? If you change the twenty-four digits in Figure 5.3 to random values and re-solve Friedmann’s equation, the probability that you’ll get a universe remaining nearly flat for 14 billion years is smaller than the probability that a dart randomly fired into space from Mars would hit the bull’s-eye on a dartboard on Earth. Yet Friedmann’s Big Bang model offers no explanation for this coincidence.2
Figure 5.3: Another unexplained mystery in Friedmann’s Big Bang model is why our Universe has lasted so long without getting severely curved and undergoing a Big Crunch or Big Chill. Each curve corresponds to a slightly different density when our Universe was a billionth of a second old. The borderline situation we’re in is highly unstable: changing merely the very last of the twenty-four digits would have triggered a Big Crunch or a Big Chill before our Universe reached 4% of its current age. (Figure idea courtesy of Ned Wright)
Surely, Alan Guth argued, there must be some mechanism that caused our Universe to have exactly the right density required for extreme flatness early on.
* * *
1We haven’t even measured the strength of gravity accurately enough to know what more than the first four of these digits need to be, so the last twenty digits are my guess for illustration.
2As pointed out by Phillip Helbig and others, the flatness problem is often misrepresented and overstated, but it remains extremely serious because of the cosmic clumpiness we discussed in the last chapter, which causes random departures from flatness early on.
How Inflation Works
The Power of Doubling
Alan’s radical insight was that by making just one strange-sounding assumption, you can solve both the horizon problem and the flatness problem in one fell swoop—and explain a lot more as well. This assumption is that once upon a time, there was a tiny uniform blob of a substance whose density was very hard to dilute. This means that if one gram of this substance expanded into twice the volume, its density (its mass per volume) would remain basically unchanged, so that you’d now have about two grams of the stuff. Compare this with a normal substance such as air: if it expands into a larger volume (as when you release compressed air from a tire), then the total number of molecules stays the same, so the total mass remains the same and the density drops.
According to Einstein’s theory of gravity, such a tiny nondiluting blob can undergo a most remarkable explosion that Alan called inflation, in effect creating a Big Bang! As illustrated in Figure 5.4, Einstein’s equations have a solution where each part of this blob doubles its size at regular time intervals, a type of growth that mathematicians refer to as exponential. In this scenario, our baby Universe grew very much the way you yourself did right after your conception (see Figure 5.5): each of your cells doubled roughly daily, causing your total number of cells to increase day by day as 1, 2, 4, 8, 16, etc. Repeated doubling is a powerful process, so your Mom would have been in trouble if you’d kept doubling your weight every day until you were born: after nine months (about 274 doublings), you’d have weighed more than all the matter in our observable Universe combined! Crazy as it sounds, this is exactly what Alan’s inflation process does: starting out with a speck much smaller and lighter than an atom, it repeatedly doubles its size until it’s more massive than our entire observable Universe.
Figure 5.4: According to Einstein’s theory of gravity, a substance whose density is undilutable can “inflate,” doubling its size at regular intervals, growing from a subatomic scale to a size vastly larger than our observable Universe in a split second and effectively putting the bang into our Big Bang. This repeated doubling occurs in all three dimensions, so that doubling the diameter makes the volume eight times larger. Here, I’ve drawn only two dimensions just for illustration, where doubling the diameter quadruples the volume.
Figure 5.5: The inflation theory says that our baby Universe grew much like a human baby: an accelerating growth phase where the size doubled at regular intervals was followed by a more leisurely decelerating growth phase. Amusingly, the vertical axis is the same for the two plots: in the simplest model, our Universe stopped inflating when it was about the size of an orange (but weighed about 1081 times more). Our baby Universe doubled its size about 1043 times faster than the first cells of the baby.
Click here to see a larger image.
Problems Solved
As you can see in Figure 5.4, repeated doubling of the size automatically causes repeated doubling of the expansion speed, which I’ve indicated by arrows. In other words, it causes accelerated expansion. If you’d really kept doubling your mass daily until birth, then you’d have expanded quite slowly initially (by just a few cell sizes per day). But toward the end of your gestation period when you weighed more than our observable Universe and doubled daily, you’d have expanded with a mind-bogglingly large speed of many billion light-years per day. Whereas you used to double your mass once per day, our inflating baby Universe doubled its mass extremely often—in some of the most popular versions of inflation, one mass doubling occurred about every ten trillionths of a trillionth of a quadrillionth (10−38) of a second, and about 260 mass doublings were required to create all the mass in our observable Universe. This means that the whole inflation process, from beginning to end, could have been almost instantaneous by human standards, requiring less than about 10−35 seconds, less time than light takes to travel a trillionth of the size of a proton. In other words, exponential expansion takes something tiny that isn�
��t moving much and turns it into a humongous, fast-expanding explosion. In this way, inflation solves the “Bang problem,” explaining what caused our Big Bang: it was caused by this repeated doubling process. It also explains why the expansion is uniform, as Edwin Hubble discovered: Figure 5.4 illustrates that regions that are twice as far from each other move apart twice as fast.
Figure 5.5 illustrates that, just as you eventually replaced your exponential body expansion by more leisurely growth, our baby Universe eventually stopped inflating. The inflating material decayed into ordinary matter which kept expanding at a more relaxed pace, coasting along with the speed it got from the explosive inflationary phase, gradually decelerated by gravity.
Alan Guth realized that inflation also solves the horizon problem. The distant regions A and B in Figure 5.2 were extremely close together during the early stages of inflation, so they had time to interact back then. The explosive expansion of inflation then brought A and B out of contact with each other, and they’re only now beginning to come back into contact. A cell in your nose has the same DNA as a cell in your toe because they have a common progenitor: they’re both produced by successive doublings of your very first cell. In the same way, distant regions of our cosmos have similar properties because they have a common origin: they’re produced by successive doublings of that same tiny speck of inflating matter.
