The cosmological constant and the pulsating universe

Abstract

The author's recently described method for obtaining an upper bound for a recollapsing, closed universe with a positive cosmological constant is extended to obtain a lower bound for a negativeA. The bounds are readily generalized to cosmologies of higher dimensions. As the radius of recollapse becomes infinite and the metric Minkowskian, the bounds shrink to zero. It is inferred that in a special relativistic theory, the cosmological term should vanish. A special relativistic proof of this is given based on requiring invariance under the «tilting» of the spacelike hypersurface. There is a discussion of the significance of this «guardian symmetry» for the self-stress problems of classical electron theory as well as the possibility of breaking supersymmetry without engendering a cosmological term. A brief application is given to the regularization of the Casimir effect. Some of the remaining problems and possible successes of the pulsating universe are also described. In the appendix, the well-known instability of the Einstein universe is briefly treated by the method used here to obtain bounds on the cosmological constant.