Relativity Lite

Cosmology | 91 One theory is that Dark Energy is what is known as the cosmological constant , a fudge factor Λ that Einstein added to his theory in 1917 to prevent an outward expansion and, thus, to match what nearly everyone believed was a static universe. He later told George Gamow “that the introduction of the cosmological term was the biggest blunder he ever made in his life.” * There is a second Friedmann equation † that gives the acceleration, A , of the universe, defined as the change in the speed of expansion, S , with time, A G c p R = − +     4 3 3 2 π ρ (5) where ρ is the conventional and dark matter density and p is the pressure of the universe. Einstein had wanted a static universe, one that did not change speed, so he would need A = 0 . The most obvious ways one could do that is to have both ρ and p = 0 or R = 0. But the first idea is no good because this is a universe with nothing in it. The second is no better since it constitutes no universe to speak of. The better solution that apparently came to Einstein was to postulate a substance pervading the universe that has negative pressure of just the right size that the term in parentheses in equation (5) is 0. That is, at the present moment in time, A G c p R G c c 0 0 2 0 0 0 2 0 2 4 3 3 4 3 3 3 = − +     = − + −     π ρ π ρ ρ      = R 0 0 (6) This solution saw the light of day for only a few years before observations showed that the universe was expanding, undermining the need for a static solution. Although this solution seems to do what Einstein wanted, it is highly unstable. If the universe were to shrink ever so slightly, the matter density would increase by a tiny fac- tor, but the negative pressure of the substance pervading all space would not change. This increase in the matter density would pull the matter further inward, again increasing the matter density, and so on, and one would ultimately have a runaway collapse of the universe. Or if the universe were to expand ever so slightly, the matter density would decrease by a tiny factor but the negative pressure of the substance pervading all space would not change. This disbursement of the matter to a larger volume would have less of an inward gravitational tug, allowing the matter to move farther apart, again decreasing the matter density, and so on, and one would ultimately have a runaway expansion of the universe. Al- though this instability would have proved a disaster for Einstein’s attempt at finding a static solution for the universe, it is just what one needs for a runaway expansion of the universe like that observed in 1998. In this case, we want a version of equation (6) whose acceleration, radius, and mass density can change with time. Also, the negative pressure (the interior parenthesis on the * George Gamow, My World Line, an Informal Autobiography (Viking Press, New York, 1970), p. 44. † Tai L. Chow, Gravity, Black Holes, and the Very Early Universe an Introduction to General Relativity and Cosmology (Springer, New York, 2008), p. 142, eq. (8.36–37).