**THE FABRIC of the COSMOS,****Brian Greene,**2004

```(annotated and with added

**bold highlights by Epsilon=One**)

**Chapter 11 - Quanta in the Sky with Diamonds**

Creating a Universe

With such progress, physicists have been motivated to see how much further inflationary cosmology can go. Can it, for example, resolve the ultimate mystery, encapsulated in

A related but somewhat less ambitious question, one that has also been asked in various guises through the ages, is:

To understand how, think of a huge but flexible box filled with many thousands of swarming children, incessantly running and jumping. Imagine that the box is completely impermeable, so no heat or energy can escape, but because it's flexible, its walls can move outward. As the children relentlessly slam into each of the box's walls — hundreds at a time, with hundreds more immediately to follow — the box steadily expands. Now, you might expect that because the walls are impermeable, the total energy embodied by the swarming children will stay fully within the expanding box. After all, where else could their energy go? Well, although a reasonable proposition, it's not quite right. There is some place for it to go. The children expend energy every time they slam into a wall, and much of this energy is transferred to the

Even though space doesn't have walls, a similar kind of energy transfer takes place as the universe expands. Just as the fast-moving children work against the inward force exerted by the box's walls as it expands, the fast-moving particles in our universe work against an inward force as space expands: They work against the inward force of gravity. And just as the total energy embodied by the children drops because it's continuously transferred to the energy of the walls as the box expands, the total energy carried by ordinary particles of matter and radiation drops because it is continually

Let's now modify our analogy a bit to gain insight into how an inflaton field impacts our description of energy exchange as space expands. Imagine that a few pranksters among the children hook up

This modified scenario is relevant to cosmology because, as we've learned, like the pranksters' rubber bands, a uniform inflaton field exerts a negative pressure within an (sic.) expanding universe. And so, just as the total energy embodied by the rubber bands increases as the box expands because they extract energy from the box's walls, the total energy embodied by the inflaton field increases as the universe expands because it

To summarize:

The pivotal nature of these observations becomes clear when we try to explain the origin of the matter and radiation that make up galaxies, stars, and everything else inhabiting the cosmos. In the standard big bang theory, the mass/energy carried by matter and radiation has steadily decreased as the universe has expanded, and so the mass/energy in the early universe greatly exceeded what we see today. Thus, instead of offering an explanation for where all the mass/energy currently inhabiting the universe originated, the standard big bang fights an unending uphill battle: the farther back the theory looks, the

In inflationary cosmology, though, much the opposite is true. Recall that the inflatioriary theory argues that matter and radiation were produced at the end of the inflationary phase as the inflaton field released its pent-up energy by rolling from perch to valley in its potential-energy bowl. The relevant question, therefore, is whether, just as the inflationary phase was drawing to a close, the theory can account for the inflaton field embodying the

The answer to this question is that inflation can, without even breaking a sweat. As just explained, the inflaton field is a gravitational parasite — it feeds on gravity — and so the total energy the inflaton field carried increased as space expanded. More precisely, the mathematical analysis shows that the energy

Thus, in stark contrast to the standard big bang theory in which the total mass/energy of the early universe was huge beyond words, inflationary cosmology, by "mining" gravity, can produce

**Leibniz's question of why there is a universe at all?**Well; at least**with our current level of understanding, that's asking for too much.**Even if a cosmological theory were to make headway on this question,**we could ask why that particular theory — its assumptions, ingredients, and equations — was relevant**, thus merely pushing the question of origin one step further back.**If logic alone**somehow**required the universe to exist and to be governed by a unique set of laws with unique ingredients,**then perhaps**we'd have a convincing story.**But,**to date, that's nothing but a pipe dream.**A related but somewhat less ambitious question, one that has also been asked in various guises through the ages, is:

**Where did all the mass/energy making up the universe come from?**Here, although inflationary cosmology does not provide a complete answer, it has cast the question in an intriguing new light.To understand how, think of a huge but flexible box filled with many thousands of swarming children, incessantly running and jumping. Imagine that the box is completely impermeable, so no heat or energy can escape, but because it's flexible, its walls can move outward. As the children relentlessly slam into each of the box's walls — hundreds at a time, with hundreds more immediately to follow — the box steadily expands. Now, you might expect that because the walls are impermeable, the total energy embodied by the swarming children will stay fully within the expanding box. After all, where else could their energy go? Well, although a reasonable proposition, it's not quite right. There is some place for it to go. The children expend energy every time they slam into a wall, and much of this energy is transferred to the

*wall's motion.*The very expansion of the box absorbs, and hence depletes, the children's energy.Even though space doesn't have walls, a similar kind of energy transfer takes place as the universe expands. Just as the fast-moving children work against the inward force exerted by the box's walls as it expands, the fast-moving particles in our universe work against an inward force as space expands: They work against the inward force of gravity. And just as the total energy embodied by the children drops because it's continuously transferred to the energy of the walls as the box expands, the total energy carried by ordinary particles of matter and radiation drops because it is continually

*transferred to gravity*as the universe expands. In short, by drawing an analogy between the inward force exerted by the box's walls and the inward force exerted by gravity (an analogy that can be established mathematically), we conclude that gravity depletes the energy in fast-moving particles of matter and radiation as space swells. The loss of energy from fast-moving particles from cosmic expansion has been confirmed by observations of the microwave background radiation. *Let's now modify our analogy a bit to gain insight into how an inflaton field impacts our description of energy exchange as space expands. Imagine that a few pranksters among the children hook up

**a number of enormous rubber bands between each of the opposite, outward-moving walls of the box.**The rubber bands exert an inward, negative pressure on the box walls, which has exactly the opposite effect of the children's outward, positive pressure; rather than transferring energy to the expansion of the box, the rubber bands' negative pressure "saps" energy from the expansion. As the box expands, the rubber bands get increasingly taut, which means they embody increasing amounts of energy.This modified scenario is relevant to cosmology because, as we've learned, like the pranksters' rubber bands, a uniform inflaton field exerts a negative pressure within an (sic.) expanding universe. And so, just as the total energy embodied by the rubber bands increases as the box expands because they extract energy from the box's walls, the total energy embodied by the inflaton field increases as the universe expands because it

*extracts energy from gravity.***To summarize:

*as the universe expands, matter and radiation lose energy to gravity while an inflaton field gains energy from gravity.*The pivotal nature of these observations becomes clear when we try to explain the origin of the matter and radiation that make up galaxies, stars, and everything else inhabiting the cosmos. In the standard big bang theory, the mass/energy carried by matter and radiation has steadily decreased as the universe has expanded, and so the mass/energy in the early universe greatly exceeded what we see today. Thus, instead of offering an explanation for where all the mass/energy currently inhabiting the universe originated, the standard big bang fights an unending uphill battle: the farther back the theory looks, the

*more*mass/energy it must somehow explain.In inflationary cosmology, though, much the opposite is true. Recall that the inflatioriary theory argues that matter and radiation were produced at the end of the inflationary phase as the inflaton field released its pent-up energy by rolling from perch to valley in its potential-energy bowl. The relevant question, therefore, is whether, just as the inflationary phase was drawing to a close, the theory can account for the inflaton field embodying the

*stupendous*quantity of mass/energy necessary to yield the matter and radiation in today's universe.The answer to this question is that inflation can, without even breaking a sweat. As just explained, the inflaton field is a gravitational parasite — it feeds on gravity — and so the total energy the inflaton field carried increased as space expanded. More precisely, the mathematical analysis shows that the energy

*density*of the inflaton field remained constant throughout the inflationary phase of rapid expansion, implying that the total energy it embodied grew in direct proportion to the volume of the space it filled. In the previous chapter, we saw that the size of the universe increased by at least a factor of 10^30 during inflation, which means the volume of the universe increased by a factor of at least (10^30)3 = 10^90. Consequently, the energy embodied in the inflaton field*increased*by the same huge factor: as the inflationary phase drew to a close, a mere 10^-35 or so seconds after it began, the energy in the inflaton field grew by a factor on the order of 10^90, if not more.*This means that at the onset of inflation, the inflaton field didn't need to have much energy, since the enormous expansion it was about to spawn would enormously amplify the energy it carried.***A simple calculation shows that a tiny nugget, on the order of 10^-26 centimeters across, filled with a uniform inflaton field — and weighing a mere***twenty pounds*— would, through the ensuing inflationary expansion, acquire enough energy to account for all we see in the universe today.*2*Thus, in stark contrast to the standard big bang theory in which the total mass/energy of the early universe was huge beyond words, inflationary cosmology, by "mining" gravity, can produce

**all the ordinary matter and radiation in the universe from a tiny, twenty-pound speck of inflaton filled space.**By no means does this answer Leibniz's question of why there is something rather than nothing, since**we've yet to explain why there is an inflaton or even the space it occupies.**But the something in need of explanation weighs a whole lot less than my dog Rocky, and that's**certainly a very different starting point than envisaged in the standard big bang.****** As the universe expands, the energy loss of photons can be directly observed because their wavelengths stretch — they undergo redshift — and the longer a photon's wavelength, the less energy it has. The microwave background photons have undergone such redshift for nearly 14 billion years, explaining their long — microwave — wavelengths, and their low temperature. Matter undergoes a similar loss of its kinetic energy (energy from particle motion), but the total energy bound up in the mass of particles (their rest energy — the energy equivalent of their mass, when at rest) remains constant.

** While useful, the rubber-band analogy is not perfect. The inward, negative pressure exerted by the rubber bands impedes the expansion of the box, whereas the inflaton's negative pressure drives the expansion of space. This important difference illustrates the clarification emphasized on page 278: in cosmology, it is not that uniform negative pressure drives expansion (only pressure differences result in forces, so uniform pressure, whether positive or negative, exerts no force). Rather, pressure, like mass, gives rise to a gravitational force. And negative pressure gives rise to a repulsive gravitational force that drives expansion. This does not affect our conclusions.

*** Some researchers, including Alan Guth and Eddie Farhi, have investigated whether one might, hypothetically, create a new universe in the laboratory by synthesizing a nugget of inflaton field. Beyond the fact that we still don't have direct experimental verification that there is suclh a thing as an inflaton field, note that the twenty pounds of inflaton field would need to be crammed in a tiny space, roughly 10^-26 or so centimeters on a side, and hence the density would be enormous — some 10^67 times the density of an atomic nucleus — way beyond what we can produce, now or perhaps ever.

** While useful, the rubber-band analogy is not perfect. The inward, negative pressure exerted by the rubber bands impedes the expansion of the box, whereas the inflaton's negative pressure drives the expansion of space. This important difference illustrates the clarification emphasized on page 278: in cosmology, it is not that uniform negative pressure drives expansion (only pressure differences result in forces, so uniform pressure, whether positive or negative, exerts no force). Rather, pressure, like mass, gives rise to a gravitational force. And negative pressure gives rise to a repulsive gravitational force that drives expansion. This does not affect our conclusions.

*** Some researchers, including Alan Guth and Eddie Farhi, have investigated whether one might, hypothetically, create a new universe in the laboratory by synthesizing a nugget of inflaton field. Beyond the fact that we still don't have direct experimental verification that there is suclh a thing as an inflaton field, note that the twenty pounds of inflaton field would need to be crammed in a tiny space, roughly 10^-26 or so centimeters on a side, and hence the density would be enormous — some 10^67 times the density of an atomic nucleus — way beyond what we can produce, now or perhaps ever.