Rick's Cosmology Tutorial: Chapter 2 Abstract

It is shown that the size of any finite portion of the universe shrinks to zero at the time of the Big Bang. This observation is the motivation for the Big Bang concept. It implies that the universe started in a state of infinite density. It is shown that the density is inevitably equal to the critical density, as derived in Chapter 1, at sufficiently early times. The net energy within a given region is the sum of the kinetic energy of the matter, plus the energy of the radiation, plus the (negative) gravitational potential energy. If this net energy is positive, or zero, then it is shown here that the ratio of the mean density of the universe to the critical density reduces monotonically from its initial value of virtually unity, and becomes asymptotic to zero at late times. In other words, the universe expands forever. In contrast, if the net energy is negative, then the ratio of the mean density to the critical density is shown to increase monotonically from virtually unity to a singularity when the universe reaches a maximum size. It then reduces monotonically back to unity at a Big Crunch.

Uses: The variation of the density with time in the primordial universe is key to subsequent predictions of the Big Bang theory. No relativity required.

Warning: Only if the universe is finite does it start as a point at the Big Bang. It the universe is infinite, then it was always infinite. See the FAQ for further details as regards an infinite universe. Dark energy is ignored in this Chapter.

Type II (core-collapse) supernova HST SN 1987A, photo taken on its 20th anniversary (2007), P. Challis, and R. Kirshner (Hubble, NASA/ESA)