ar X iv : a st ro - p h / 01 11 42 5 v 1 2 1 N ov 2 00 1 Resolution of Cosmological Singularity and a Plausible Mechanism of the Big Bang

The initial cosmological singularity in the framework of the general theory of relativity is resolved by introducing the effect of the uncertainty principle of quantum theory without violating conventional laws of physics. A plausible account of the mechanism of the big bang, analogous to that of a nuclear explosion, is given and the currently accepted Planck temperature of ∼ 10 32 K at the beginning of the big bang is predicted. Subj-class: cosmology: theory-pre-big bang; mechanism of the big bang. I. Introduction. The standard hot Big Bang model within the framework of the general theory of relativity has been spectacularly successful in describing the evolution of the universe from ten thousandth of a second after the big bang to the present time. Nevertheless, the occurrence of the initial singularity, a state of infinite density and temperature, preceding the big bang as shown by the theorems [1,2] of Penrose and of Hawking and Penrose, raises some of the deepest questions concerning the foundation of this model of cosmology. To resolve this problem, we propose that during the process of the gravitational collapse of the universe, in the domain of the infinitesimally small region of space-time around the initial singularity, the general theory of relativity by itself is incomplete and the introduction of the effect of quantum theory becomes absolutely necessary. Therefore it is assumed that at the end of the gravitational collapse, without violating the uncertainty principle, the total mass of the universe including all forms of energy condensed into the primordial black hole (PBH) in a state of ∼ absolute zero temperature. The reasoning for this assumption is consistent with Penrose's argument based on thermodynamic considerations that the universe was initially very regular (i.e., in a state of zero entropy); Chandrasekhar [3] likewise agreed with Penrose's view, contrary to those who hold that the chaos at the initial singularity was maximal. II. Quantization of energy. The energy of the collapsed state of the universe (PBH), in light of the above argument, is quantized in such a manner that each quantum of mass (frozen energy) is characterized by the fundamental constants of the general theory of relativity and of quantum theory (namely G, ¯ h, c). For this purpose the principle of dimensional analysis and the reciprocity relation, analogous to that of the unitarity condition of quantum theory, are incorporated into our method of quantization. Consequently, the physical properties of the …