DeWitt's Wave Function of the Universe

Vitaly Kuyukov

Space-time and universal wave function

Frank J. Tipler

David Craig, Parampreet Singh

We give an explicit, rigorous framework for calculating quantum probabilities in a model theory of quantum gravity. Specifically, we construct the decoherence functional for the Wheeler-DeWitt quantization of a flat Friedmann-Robertson-Walker cosmology with a free, massless, minimally coupled scalar field, thus providing a complete decoherent histories formulation for this quantum cosmological model. The decoherence functional is applied to study predictions concerning the model's Dirac (relational) observables; the behavior of semiclassical states and superpositions of such states; and to study the singular behavior of quantum Wheeler-DeWitt universes. Within this framework, rigorous formulas are given for calculating the corresponding probabilities from the wave function when those probabilities may be consistently defined, thus replacing earlier heuristics for interpreting the wave function of the universe with explicit constructions. It is shown according to a rigorously formulated standard, and in a quantum-mechanically consistent way, that in this quantization these models are generically singular. Independent of the choice of state we show that the probability for these Wheeler-DeWitt quantum universes to ever encounter a singularity is unity. In addition, the relation between histories formulations of quantum theory and relational Dirac observables is clarified.

Raymond Laflamme

Alexander Vilenkin

A probabilistic interpretation of the wave function of the Universe is proposed in which ``probability'' and ``unitarity'' are inherently approximate concepts. Their validity is limited by the accuracy of the semiclassical approximation for the entire Universe. This approach (which is a logical extension of DeWitt's) defines a positive-semidefinite probability distribution and satisfies the correspondence principle with classical cosmology and with quantum mechanics. In particular, one recovers the standard probabilistic interpretation of the wave function for a small subsystem of the Universe.

Chrsquo, Ch’ng Han Siong, Shahidan Radiman

Friedmann equations play a central role in cosmology for describing the evolution of the universe. Initially, the Friedmann equations were derived by Alexander Friedmann in 1922. He derived the equations from Einstein’s field equations for a universe which is spatially homogeneous and isotropic. The equations were again derived from Newtonian mechanics by Milne. However in this paper, we derive the spatially flat Friedmann equation from Wheeler-DeWitt equation. We apply the Bohm-de Broglie interpretation to the wave function of universe. In addition, we also set a condition to the wave function, where a large scale factor of the universe is needed.   Key words: Canonical quantum cosmology, Friedmann equations, Wheeler-DeWitt equation.