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Inflation and the Horizon Problem

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  • Inflation and the Horizon Problem

    THE FABRIC of the COSMOS, Brian Greene, 2004
    ```(annotated and with added bold highlights by Epsilon=One)
    Chapter 10 - Deconstructing the Bang
    Inflation and the Horizon Problem
    One such problem is called the horizon problem and concerns the uniformity of the microwave background radiation that we came across previously. Recall that the temperature of the microwave radiation reaching us from one direction in space agrees with that coming from any other direction to fantastic accuracy (to better than a thousandth of a degree). This observational fact is pivotal, because it attests to homogeneity throughout space, allowing for enormous simplifications in theoretical models of the cosmos. In earlier chapters, we used this homogeneity to narrow down drastically the possible shapes for space and to argue for a uniform cosmic time. The problem arises when we try to explain how the universe became so uniform. How is it that vastly distant regions of the universe have arranged themselves to have nearly identical temperatures?

    If you think back to Chapter 4, one possibility is that just as nonlocal quantum entanglement can correlate the spins of two widely separated particles, maybe it can also correlate the temperatures of two widely separated regions of space. While this is an interesting suggestion, the tremendous dilution of entanglement in all but the most controlled settings, as discussed at the end of that chapter, essentially rules it out. Okay, perhaps there is a simpler explanation. Maybe a long time ago when every region of space was nearer to every other, their temperatures equalized through their close contact much as a hot kitchen and a cool living room come to the same temperature when a door between them is opened for a while. In the standard big bang theory, though, this explanation also fails. Here's one way to think about it.

    Imagine watching a film that depicts the full course of cosmic evolution from the beginning until today. Pause the film at some arbitrary moment and ask yourself: Could two particular regions of space, like the kitchen and the living room, have influenced each other's temperature? Could they have exchanged light and heat? The answer depends on two things: The distance between the regions and the amount of time that has elapsed since the bang. If their separation is less than the distance light could have traveled in the time since the bang, then the regions could have influenced each other; otherwise, they couldn't have. Now, you might think that all regions of the observable universe could have interacted with each other way back near the beginning because the farther back we wind the film, the closer the regions become and hence the easier it is for them to interact. But this reasoning is too quick; it doesn't take account of the fact that not only were regions of space closer, but there was also less time for them to have communicated.

    To do a proper analysis, imagine running the cosmic film in reverse while focusing on two regions of space currently on opposite sides of the observable universe — regions that are so distant that they are currently beyond each other's spheres of influence. If in order to halve their separation we have to roll the cosmic film more than halfway back toward the beginning, then even though the regions of space were closer together, communication between them was still impossible: they were half as far apart, but the time since the bang was less than half of what it is today, and so light could travel only less than half as far. Similarly, if from that point in the film we have to run more than halfway back to the beginning in order to halve the separation between the regions once again, communication becomes more difficult still. With this kind of cosmic evolution, even though regions were closer together in the past, it becomes more puzzling — not less — that they somehow managed to equalize their temperatures. Relative to how far light can travel, the regions become increasingly cut off as we examine them ever farther back in time.

    This is exactly what happens in the standard big bang theory. In the standard big bang, gravity acts only as an attractive force, and so, ever since the beginning, it has been acting to slow the expansion of space. Now, if something is slowing down, it will take more time to cover a given distance. For instance, imagine that Secretariat left the gate at a blistering pace and covered the first half of a racecourse in two minutes, but because it's not his best day, he slows down considerably during the second half and takes three more minutes to finish. When viewing a film of the race in reverse, we'd have to roll the film more than halfway back in order to see Secretariat at the course's halfway mark (we'd have to run the five-minute film of the race all the way back to the two-minute mark). Similarly, since in the standard big bang theory gravity slows the expansion of space, from any point in the cosmic film we have to wind more than halfway back in time in order to halve the separation between two regions. And, as above, this means that even though the regions of space were closer together at earlier times, it was more difficult — not less — for them to influence each other and hence more puzzling — not less — that they somehow reached the same temperature.

    Physicists define a region's cosmic horizon (or horizon for short) as the most distant surrounding regions of space that are close enough to the given region for the two to have exchanged light signals in the time since the bang. The analogy is to the most distant things we can see on earth's surface from any particular vantage point. 15 The horizon problem, then, is the puzzle, inherent in the observations, that regions whose horizons have always been separate — regions that could never have interacted, communicated, or exerted any kind of influence on each other — somehow have nearly identical temperatures.

    The horizon problem does not imply that the standard big bang model is wrong, but it does cry out for explanation. Inflationary cosmology provides one.

    In inflationary cosmology, there was a brief instant during which gravity was repulsive and this drove space to expand faster and faster. During this part of the cosmic film, you would have to wind the film less than halfway back in order to halve the distance between two regions. Think of a race in which Secretariat covers the first half of the course in two minutes and, because he's having the run of his life, speeds up and blazes through the second half in one minute. You'd only have to wind the three-minute film of the race back to the two-minute mark — less than halfway back — to see him at the course's halfway point. Similarly, the increasingly rapid separation of any two regions of space during inflationary expansion implies that halving their separation requires winding the cosmic film less — much less — than halfway back toward the beginning. As we go farther back in time, therefore, it becomes easier for any two regions of space to influence each other, because, proportionally speaking, there is more time for them to communicate. Calculations show that if the inflationary-expansion phase drove space to expand by at least a factor of 10^30, an amount that is readily achieved in specific realizations of inflationary expansion, all the regions in space that we currently see — all the regions in space whose temperatures we have measured — were able to communicate as easily as the adjacent kitchen and living room and hence efficiently come to a common temperature in the earliest moments of the universe. 16 In a nutshell, space expands slowly enough in the very beginning for a uniform temperature to be broadly established and then, through an intense burst of ever more rapid expansion, the universe makes up for the sluggish start and widely disperses nearby regions.

    That's how inflationary cosmology explains the otherwise mysterious uniformity of the microwave background radiation suffusing space.
    Last edited by Reviewer; 10-13-2012, 07:08 AM.