Department of Mathematics

In this talk I explore the possibility that the explosion of the Big Bang that caused the outward motion of the galaxies, was an explosion of finite total mass, instead of the infinite mass explosion inherent in the standard model of cosmology based on the Friedmann universe. The discussion is based on recent joint work with J. Smoller, (Proc. Nat. Acad. Sci., USA, Vol. 100, no. 20, pp. 11216-11218), in which we introduce a new exact solution of the Einstein equations in which the explosion of the Big Bang generates an outgoing, spherical, entropy satisfying shock wave that emerges from the center of the explosion at the instant of the Big Bang, (like the blast wave of a nuclear explosion), and the expanding galaxies correspond to the region inside the wave. What is new here is that when the shock wave is far enough out to be consistent with astronomical observations, (beyond one Hubble length - the distance light can travel since the Big Bang explosion), the whole explosion begins inside a (time reversed) Black Hole - a White Hole in which everything is running backwards, exploding outward instead of collapsing inward. For this, we introduce a new metric which we call the TOV metric inside the Black Hole which cuts off the mass at a finite value, and matches Lipschitz continuously to the Freidmann metric at the shock wave. In our model, the universe eventually emerges from the Black Hole, and from then on expands like an Oppenheimer-Snyder solution - a finite ball of matter expanding into empty space. We are inside the explosion, but to an observer in the far field beyond the shock wave, this would look like a giant supernova explosion. It also follows from our model that information about the shock wave propagates inward from the shock wave, into a large central region of uniform expansion - and thus to an observer (like us) on the inside of the "bubble", everything would look exactly like the Friedmann universe up until the time when the shock wave comes into view from the farthest field of observations. In particular, up until the shock wave comes into view, everything looks the same as in the Friedmann model. In this talk I will discuss the mathematical derivation of this solution, and point out a number of surprises that one could not have anticipated ahead of time -- including the unexpected emergence of the correct equation of state at the Big Bang, the breaking of the time symmetry by the entropy condition, and interesting mathematical consequences of the reversal of space and time inside the Black Hole. (Articles and commentaries can be found on authors website: http://www.math.ucdavis.edu/~temple/articles/).