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THE FABRIC of the COSMOS, Brian Greene, 2004
```(annotated and with added bold highlights by Epsilon=One)
```(annotated and with added bold highlights by Epsilon=One)
Chapter 10 - Deconstructing the Bang
Inflation
Well, here's why. Although a supercooled Higgs field shares certain features with a cosmological constant, Guth realized that they are not completely identical. Instead, there are two key differences — differences that make all the difference.
Figure 10.1 (a): A supercooled Higgs field is one whose value gets trapped on the energy bowl's high-energy plateau, like the frog on a bump. (b) Typically, a supercooled Higgs field will quickly find its way off the plateau and drop to a value with lower energy, like the frog's jumping off the bump.
First, whereas a cosmological constant is constant — it does not vary with time, so it provides a constant, unchanging outward push — a supercooled Higgs field need not be constant. Think of a frog perched on the bump in Figure 10.1a. It may hang out there for a while, but sooner or later a random jump this way or that — a jump taken not because the bowl is hot (it no longer is), but merely because the frog gets restless — will propel the frog beyond the bump, after which it will slide down to the bowl's lowest point, as in Figure 10.1b. A Higgs field can behave similarly. Its value throughout all of space may get stuck on its energy bowl's central bump while the temperature drops too low to drive significant thermal agitation. But quantum processes will inject random jumps into the Higgs field's value, and a large enough jump will propel it off the plateau, allowing its energy and pressure to relax to zero. 10 Guth's calculations showed that, depending on the precise shape of the bowl's bump, this jump could have happened rapidly, perhaps in as short a time as .00000000000000000000000000000001 (10^-35) seconds. Subsequently, Andrei Linde, then working at the Lebedev Physical Institute in Moscow, and Paul Steinhardt, then working with his student Andreas Albrecht at the University of Pennsylvania, discovered a way for the Higgs field's relaxation to zero energy and pressure throughout all of space to happen even more efficiently and significantly more uniformly (thereby curing certain technical problems inherent to Guth's original proposal 11). They showed that if the potential energy bowl had been smoother and more gradually sloping, as in Figure 10.2, no quantum jumps would have been necessary: the Higgs field's value would quickly roll down to the valley, much like a ball rolling down a hill. The upshot is that if a Higgs field acted like a cosmological constant, it did so only for a brief moment.
Figure 10.2: A smoother and more gradually sloping bump allows the Higgs field value to roll down to the zero-energy valley more easily and more uniformly throughout space.
The second difference is that whereas Einstein carefully and arbitrarily chose the value of the cosmological constant — the amount of energy and negative pressure it contributed to each volume of space — so that its outward repulsive force would precisely balance the inward attractive force arising from the ordinary matter and radiation in the cosmos, Guth was able to estimate the energy and negative pressure contributed by the Higgs fields he and Tye had been studying. And the answer he found was more than
times larger than the value Einstein had chosen. This number is huge, obviously, and so the outward push supplied by the Higgs field's repulsive gravity is monumental compared with what Einstein envisioned originally with the cosmological constant.
Now, if we combine these two observations — that the Higgs field will stay on the plateau, in the high-energy, negative-pressure state, only for the briefest of instants, and that while it is on the plateau, the repulsive outward push it generates is enormous — what do we have? Well, as Guth realized, we have a phenomenal, short-lived, outward burst. In other words, we have exactly what the big bang theory was missing: a bang, and a big one at that. That's why Guth's discovery is something to get excited about. 12
The cosmological picture emerging from Guth's breakthrough is thus the following. A long time ago, when the universe was enormously dense, its energy was carried by a Higgs field perched at a value far from the lowest point on its potential energy bowl. To distinguish this, particular Higgs field from others (such as the electroweak Higgs field responsible for giving mass to the familiar particle species, or the Higgs field that arises in grand unified theories 13) it is usually called the inflaton field.* Because of its negative pressure, the inflaton field generated a gigantic gravitational repulsion that drove every region of space to rush away from every other; in Guth's language, the inflaton drove the universe to inflate. The repulsion lasted only about 10^-35 seconds, but it was so powerful that even in that brief moment the universe swelled by a huge factor. Depending on details such as the precise shape of the inflaton field's potential energy, the universe could easily have expanded by a factor of 10^30, 10^50, or 10^100 or more.
These numbers are staggering. An expansion factor of 10^30 — a conservative estimate — would be like scaling up a molecule of DNA to roughly the size of the Milky Way galaxy, and in a time interval that's much shorter than a billionth of a billionth of a billionth of the blink of an eye. By comparison, even this conservative expansion factor is billions and billions of times the expansion that would have occurred according to the standard big bang theory during the same time interval, and it exceeds the total expansion factor that has cumulatively occurred over the subsequent 14 billion years! In the many models of inflation in which the calculated expansion factor is much larger than 10^30, the resulting spatial expanse is so enormous that the region we are able to see, even with the most powerful telescope possible, is but a tiny fraction of the whole universe. According to these models, none of the light emitted from the vast majority of the universe could have reached us yet, and much of it won't arrive until long after the sun and earth have died out. If the entire cosmos were scaled down to the size of earth, the part accessible to us would be much smaller than a grain of sand.
Figure 10.3 (a) Inflationary cosmology inserts a quick, enormous burst of spatial expansion early on in the history of the universe. (b) After the burst, the evolution of the universe merges into the standard evolution theorized in the big bang model.
Roughly 10^-35 seconds after the burst began, the inflaton field found its way off the high-energy plateau and its value throughout space slid down to the bottom of the bowl, turning off the repulsive push. And as the inflaton value rolled down, it relinquished its pent-up energy to the production of ordinary particles of matter and radiation — like a foggy mist settling on the grass as morning dew — that uniformly filled the expanding space. 14 From this point on, the story is essentially that of the standard big bang theory: space continued to expand and cool in the aftermath of the burst, allowing particles of matter to clump into structures like galaxies, stars, and planets, which slowly arranged themselves into the universe we currently see, as illustrated in Figure 10.3.
Guth's discovery — dubbed inflationary cosmology — together with the important improvements contributed by Linde, and by Albrecht and Steinhardt, provided an explanation for what set space expanding in the first place. A Higgs field perched above its zero energy value can provide an outward blast driving space to swell. Guth provided the big bang with a bang.
Figure 10.1 (a): A supercooled Higgs field is one whose value gets trapped on the energy bowl's high-energy plateau, like the frog on a bump. (b) Typically, a supercooled Higgs field will quickly find its way off the plateau and drop to a value with lower energy, like the frog's jumping off the bump.
First, whereas a cosmological constant is constant — it does not vary with time, so it provides a constant, unchanging outward push — a supercooled Higgs field need not be constant. Think of a frog perched on the bump in Figure 10.1a. It may hang out there for a while, but sooner or later a random jump this way or that — a jump taken not because the bowl is hot (it no longer is), but merely because the frog gets restless — will propel the frog beyond the bump, after which it will slide down to the bowl's lowest point, as in Figure 10.1b. A Higgs field can behave similarly. Its value throughout all of space may get stuck on its energy bowl's central bump while the temperature drops too low to drive significant thermal agitation. But quantum processes will inject random jumps into the Higgs field's value, and a large enough jump will propel it off the plateau, allowing its energy and pressure to relax to zero. 10 Guth's calculations showed that, depending on the precise shape of the bowl's bump, this jump could have happened rapidly, perhaps in as short a time as .00000000000000000000000000000001 (10^-35) seconds. Subsequently, Andrei Linde, then working at the Lebedev Physical Institute in Moscow, and Paul Steinhardt, then working with his student Andreas Albrecht at the University of Pennsylvania, discovered a way for the Higgs field's relaxation to zero energy and pressure throughout all of space to happen even more efficiently and significantly more uniformly (thereby curing certain technical problems inherent to Guth's original proposal 11). They showed that if the potential energy bowl had been smoother and more gradually sloping, as in Figure 10.2, no quantum jumps would have been necessary: the Higgs field's value would quickly roll down to the valley, much like a ball rolling down a hill. The upshot is that if a Higgs field acted like a cosmological constant, it did so only for a brief moment.
Figure 10.2: A smoother and more gradually sloping bump allows the Higgs field value to roll down to the zero-energy valley more easily and more uniformly throughout space.
The second difference is that whereas Einstein carefully and arbitrarily chose the value of the cosmological constant — the amount of energy and negative pressure it contributed to each volume of space — so that its outward repulsive force would precisely balance the inward attractive force arising from the ordinary matter and radiation in the cosmos, Guth was able to estimate the energy and negative pressure contributed by the Higgs fields he and Tye had been studying. And the answer he found was more than
1000000000000000000000000000000000000
0000000000000000000000000000000000000
000000000000000000000000000 (10^100)
0000000000000000000000000000000000000
000000000000000000000000000 (10^100)
times larger than the value Einstein had chosen. This number is huge, obviously, and so the outward push supplied by the Higgs field's repulsive gravity is monumental compared with what Einstein envisioned originally with the cosmological constant.
Now, if we combine these two observations — that the Higgs field will stay on the plateau, in the high-energy, negative-pressure state, only for the briefest of instants, and that while it is on the plateau, the repulsive outward push it generates is enormous — what do we have? Well, as Guth realized, we have a phenomenal, short-lived, outward burst. In other words, we have exactly what the big bang theory was missing: a bang, and a big one at that. That's why Guth's discovery is something to get excited about. 12
The cosmological picture emerging from Guth's breakthrough is thus the following. A long time ago, when the universe was enormously dense, its energy was carried by a Higgs field perched at a value far from the lowest point on its potential energy bowl. To distinguish this, particular Higgs field from others (such as the electroweak Higgs field responsible for giving mass to the familiar particle species, or the Higgs field that arises in grand unified theories 13) it is usually called the inflaton field.* Because of its negative pressure, the inflaton field generated a gigantic gravitational repulsion that drove every region of space to rush away from every other; in Guth's language, the inflaton drove the universe to inflate. The repulsion lasted only about 10^-35 seconds, but it was so powerful that even in that brief moment the universe swelled by a huge factor. Depending on details such as the precise shape of the inflaton field's potential energy, the universe could easily have expanded by a factor of 10^30, 10^50, or 10^100 or more.
These numbers are staggering. An expansion factor of 10^30 — a conservative estimate — would be like scaling up a molecule of DNA to roughly the size of the Milky Way galaxy, and in a time interval that's much shorter than a billionth of a billionth of a billionth of the blink of an eye. By comparison, even this conservative expansion factor is billions and billions of times the expansion that would have occurred according to the standard big bang theory during the same time interval, and it exceeds the total expansion factor that has cumulatively occurred over the subsequent 14 billion years! In the many models of inflation in which the calculated expansion factor is much larger than 10^30, the resulting spatial expanse is so enormous that the region we are able to see, even with the most powerful telescope possible, is but a tiny fraction of the whole universe. According to these models, none of the light emitted from the vast majority of the universe could have reached us yet, and much of it won't arrive until long after the sun and earth have died out. If the entire cosmos were scaled down to the size of earth, the part accessible to us would be much smaller than a grain of sand.
Figure 10.3 (a) Inflationary cosmology inserts a quick, enormous burst of spatial expansion early on in the history of the universe. (b) After the burst, the evolution of the universe merges into the standard evolution theorized in the big bang model.
Roughly 10^-35 seconds after the burst began, the inflaton field found its way off the high-energy plateau and its value throughout space slid down to the bottom of the bowl, turning off the repulsive push. And as the inflaton value rolled down, it relinquished its pent-up energy to the production of ordinary particles of matter and radiation — like a foggy mist settling on the grass as morning dew — that uniformly filled the expanding space. 14 From this point on, the story is essentially that of the standard big bang theory: space continued to expand and cool in the aftermath of the burst, allowing particles of matter to clump into structures like galaxies, stars, and planets, which slowly arranged themselves into the universe we currently see, as illustrated in Figure 10.3.
Guth's discovery — dubbed inflationary cosmology — together with the important improvements contributed by Linde, and by Albrecht and Steinhardt, provided an explanation for what set space expanding in the first place. A Higgs field perched above its zero energy value can provide an outward blast driving space to swell. Guth provided the big bang with a bang.
* You might think I've left out an "i" in the last syllable of "inflaton," but I haven't; physicists often give fields names, such as photon and gluon, which end with "on."