The birth of the Universe as a result of the change of the metric signature

Abstract

In this paper, I discuss the idea that the birth of our Universe may be a result of a quantum transition from a physical continuum with the Euclidean signature to a Lorentzian spacetime. A similar idea was expressed by Andrei D. Sakharov. At the classical level, the idea was studied by George F. R. Ellis and his collaborators, who explored if solutions to the classical Einstein equation exist which admit a change of metric signature. The present paper aims at examining possible realizations of this idea at the level of quantum gravity, in the framework of the Wheeler -DeWitt theory and in the extended phase space approach to quantization of gravity. I intend to answer the questions: Does the Hartle -Hawking wave function imply such a realization? How can this idea be realized in the extended phase space approach to quantum gravity, where the change of signature is described by imposing special conditions on g 00component of the metric in different regions of the physical continuum? The conclusion is that the idea can be realized from a formal mathematical point of view, but it can hardly help in understanding how spacetime structure and time itself appeared from a timeless continuum.

Canonical quantization of modified non-gauge invariant Einstein-Maxwell gravity and stability of spherically symmetric electrostatic stars

“…As an application of loop quantum gravity approach, authors of the work [21] are studied in effects of loop quantum geometry on birth of universe via Vilenkin's tunneling wavefunction proposal. In the framework of the Wheeler-DeWitt theory of quantum gravity author of the work [22] find birth of the universe via metric signature transition. Author investigated previously, quantum cosmology of flat Robertson-Walker spacetime in ref [23] for a modified scalar-vector-tensor Brans-Dicke gravity by solving the Wheeler-DeWitt wave equation.…”