At the Edge of Time (Science Essentials) by Hooper Dan

Author:Hooper, Dan
Language: eng
Format: epub
Publisher: epubor.com

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To make it easier to understand how the process described in this homework problem may have played out in the early universe, picture a simple game. There is a game board with a large number of pieces randomly scattered across it. In each turn, each of the pieces is moved in a randomly determined direction, and if it touches another piece, both are removed from the game. At the end of each turn, the game board is stretched in all directions, increasing in area by 20 percent and pulling each of the remaining pieces away from each other.

In this game, the pieces are analogous to the particles of dark matter, which annihilate each other in pairs when they interact. And the game board is space itself, which is expanding rapidly during this early period of our universe’s history. For concreteness, let’s imagine that there are enough pieces—or particles—on the board such that 90 percent of them are removed at the end of the first turn. In the second turn, a much smaller fraction of the remaining pieces is removed. This is true for two reasons. There are ten times fewer pieces on the board, so the chance that any given piece will touch another is reduced by a factor of 10. And because the board has become bigger, this further reduces the chance that any two pieces will come into contact. At the end of the second turn, about 9.25 percent of the original pieces remain on the board, and this drops to about 7.25 percent by the end of the tenth turn. After fifty turns, just over 6.8 percent of the original pieces remain. The interesting thing is that around this time, the number of pieces on the board essentially stops changing. By this point in the game, the board is so big and the number of remaining pieces so small that you would not expect a given piece to touch another ever again, even if you played the game for an infinite number of additional turns. The number of pieces that remain on the board has simply stopped evolving. In much the same way, the abundance of dark matter in our universe may have been established through a similar process in the early universe, when it ceased to interact with both itself and with other forms of matter and energy.

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