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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 11 - Quanta in the Sky with Diamonds
Entropy and Inflation
Indeed, this is significant progress. But two important issues remain.
First, we seem to be concluding that the inflationary burst smooths things out and hence lowers total entropy, embodying a physical mechanism — not just a statistical fluke — that appears to violate the second law of thermodynamics. Were that the case, either our understanding of the second law or our current reasoning would have to be in error. In actuality, though, we don't have to face either of these options, because total entropy does not go down as a result of inflation. What really happens during the inflationary burst is that the total entropy goes up, but it goes up much less than it might have. You see, by the end of the inflationary phase, space was stretched smooth and so the gravitational contribution to entropy — the entropy associated with the possible bumpy, nonordered, nonuniform shape of space — was minimal. However, when the inflaton field slid down its bowl and relinquished its pent-up energy, it is estimated to have produced about 10^80 particles of matter and radiation. Such a huge number of particles, like a book with a huge number of pages, embodies a huge amount of entropy. Thus, even though the gravitational entropy went down, the increase in entropy from the production of all these particles more than compensated. The total entropy increased, just as we expect from the second law.
But, and this is the important point, the inflationary burst, by smoothing out space and ensuring a homogeneous, uniform, low-entropy gravitational field, created a huge gap between what the entropy contribution from gravity was and what it might have been. Overall entropy increased during inflation, but by a paltry amount compared with how much it could have increased. It's in this sense that inflation generated a low-entropy universe: by the end of inflation, entropy had increased, but by nowhere near the factor by which the spatial expanse had increased. If entropy is likened to property taxes, it would be as if New York City acquired the Sahara Desert. The total property taxes collected would go up, but by a tiny amount compared with the total increase in acreage.
Ever since the end of inflation, gravity has been trying to make up the entropy difference. Every clump — be it a galaxy, or a star in a galaxy, or a planet, or a black hole — that gravity has subsequently coaxed out of the uniformity (seeded by the tiny nonuniformity from quantum jitters) has increased entropy and has brought gravity one step closer to realizing its entropy potential. In this sense, then, inflation is a mechanism that yielded a large universe with relatively low gravitational entropy, and in that way set the stage for the subsequent billions of years of gravitational clumping whose effects we now witness. And so inflationary cosmology gives a direction to time's arrow by generating a past with exceedingly low gravitational entropy; the future is the direction in which this entropy grows. 4
The second issue becomes apparent when we continue down the path to which time's arrow led us in Chapter 6. From an egg, to the chicken that laid it, to the chicken's feed, to the plant kingdom, to the sun's heat and light, to the big bang's uniformly distributed primordial gas, we followed the universe's evolution into a past that had ever greater order, at each stage pushing the puzzle of low entropy one step further back in time. We have just now realized that an even earlier stage of inflationary expansion can naturally explain the smooth and uniform aftermath of the bang. But what about inflation itself? Can we explain the initial link in this chain we've followed? Can we explain why conditions were right for an inflationary burst to happen at all?
This is an issue of paramount importance. No matter how many puzzles inflationary cosmology resolves in theory, if an era of inflationary expansion never took place, the approach will be rendered irrelevant. Moreover, since we can't go back to the early universe and determine directly whether inflation occurred, assessing whether we've made real progress in setting a direction to time's arrow requires that we determine the likelihood that the conditions necessary for an inflationary burst were achieved. That is, physicists bristle at the standard big bang's reliance on finely tuned homogeneous initial conditions that, while observationally motivated, are theoretically unexplained. It feels deeply unsatisfying for the low-entropy state of the early universe simply to be assumed; it feels hollow for time's arrow to be imposed on the universe, without explanation. At first blush, inflation offers progress by showing that what's assumed in the standard big bang emerges from inflationary evolution. But if the initiation of inflation requires yet other, highly special, exceedingly low-entropy conditions, we will pretty much find ourselves back at square one. We will merely have traded the big bang's special conditions for those necessary to ignite inflation, and the puzzle of time's arrow will remain just as puzzling.
What are the conditions necessary for inflation? We've seen that inflation is the inevitable result of the inflaton field's value getting stuck, for just a moment and within just a tiny region, on the high-energy plateau in its potential energy bowl. Our charge, therefore, is to determine how likely this starting configuration for inflation actually is. If initiating inflation proves easy, we'll be in great shape. But if the necessary conditions are extraordinarily unlikely to be attained, we will merely have shifted the question of time's arrow one step further back — to finding the explanation for the low-entropy inflaton field configuration that got the ball rolling.
I'll first describe current thinking on this issue in the most optimistic light, and then return to essential elements of the story that remain cloudy.
First, we seem to be concluding that the inflationary burst smooths things out and hence lowers total entropy, embodying a physical mechanism — not just a statistical fluke — that appears to violate the second law of thermodynamics. Were that the case, either our understanding of the second law or our current reasoning would have to be in error. In actuality, though, we don't have to face either of these options, because total entropy does not go down as a result of inflation. What really happens during the inflationary burst is that the total entropy goes up, but it goes up much less than it might have. You see, by the end of the inflationary phase, space was stretched smooth and so the gravitational contribution to entropy — the entropy associated with the possible bumpy, nonordered, nonuniform shape of space — was minimal. However, when the inflaton field slid down its bowl and relinquished its pent-up energy, it is estimated to have produced about 10^80 particles of matter and radiation. Such a huge number of particles, like a book with a huge number of pages, embodies a huge amount of entropy. Thus, even though the gravitational entropy went down, the increase in entropy from the production of all these particles more than compensated. The total entropy increased, just as we expect from the second law.
But, and this is the important point, the inflationary burst, by smoothing out space and ensuring a homogeneous, uniform, low-entropy gravitational field, created a huge gap between what the entropy contribution from gravity was and what it might have been. Overall entropy increased during inflation, but by a paltry amount compared with how much it could have increased. It's in this sense that inflation generated a low-entropy universe: by the end of inflation, entropy had increased, but by nowhere near the factor by which the spatial expanse had increased. If entropy is likened to property taxes, it would be as if New York City acquired the Sahara Desert. The total property taxes collected would go up, but by a tiny amount compared with the total increase in acreage.
Ever since the end of inflation, gravity has been trying to make up the entropy difference. Every clump — be it a galaxy, or a star in a galaxy, or a planet, or a black hole — that gravity has subsequently coaxed out of the uniformity (seeded by the tiny nonuniformity from quantum jitters) has increased entropy and has brought gravity one step closer to realizing its entropy potential. In this sense, then, inflation is a mechanism that yielded a large universe with relatively low gravitational entropy, and in that way set the stage for the subsequent billions of years of gravitational clumping whose effects we now witness. And so inflationary cosmology gives a direction to time's arrow by generating a past with exceedingly low gravitational entropy; the future is the direction in which this entropy grows. 4
The second issue becomes apparent when we continue down the path to which time's arrow led us in Chapter 6. From an egg, to the chicken that laid it, to the chicken's feed, to the plant kingdom, to the sun's heat and light, to the big bang's uniformly distributed primordial gas, we followed the universe's evolution into a past that had ever greater order, at each stage pushing the puzzle of low entropy one step further back in time. We have just now realized that an even earlier stage of inflationary expansion can naturally explain the smooth and uniform aftermath of the bang. But what about inflation itself? Can we explain the initial link in this chain we've followed? Can we explain why conditions were right for an inflationary burst to happen at all?
This is an issue of paramount importance. No matter how many puzzles inflationary cosmology resolves in theory, if an era of inflationary expansion never took place, the approach will be rendered irrelevant. Moreover, since we can't go back to the early universe and determine directly whether inflation occurred, assessing whether we've made real progress in setting a direction to time's arrow requires that we determine the likelihood that the conditions necessary for an inflationary burst were achieved. That is, physicists bristle at the standard big bang's reliance on finely tuned homogeneous initial conditions that, while observationally motivated, are theoretically unexplained. It feels deeply unsatisfying for the low-entropy state of the early universe simply to be assumed; it feels hollow for time's arrow to be imposed on the universe, without explanation. At first blush, inflation offers progress by showing that what's assumed in the standard big bang emerges from inflationary evolution. But if the initiation of inflation requires yet other, highly special, exceedingly low-entropy conditions, we will pretty much find ourselves back at square one. We will merely have traded the big bang's special conditions for those necessary to ignite inflation, and the puzzle of time's arrow will remain just as puzzling.
What are the conditions necessary for inflation? We've seen that inflation is the inevitable result of the inflaton field's value getting stuck, for just a moment and within just a tiny region, on the high-energy plateau in its potential energy bowl. Our charge, therefore, is to determine how likely this starting configuration for inflation actually is. If initiating inflation proves easy, we'll be in great shape. But if the necessary conditions are extraordinarily unlikely to be attained, we will merely have shifted the question of time's arrow one step further back — to finding the explanation for the low-entropy inflaton field configuration that got the ball rolling.
I'll first describe current thinking on this issue in the most optimistic light, and then return to essential elements of the story that remain cloudy.