Inflationary Model of the Universe with a Type IX Metric and Possibility of Its Quantum Birth
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INFLATIONARY MODEL OF THE UNIVERSE WITH A TYPE IX METRIC AND POSSIBILITY OF ITS QUANTUM BIRTH E. V. Kufshinova
UDC 530.12:531.551
Within the framework of the general theory of relativity, an anisotropic cosmological model with expansion and rotation with a Bianchi type IX metric is constructed. The first stage of inflation of a Universe filled with a scalar field and an anisotropic liquid is considered. The Wheeler–De Witt equation is obtained, and the possibility of minisuperspace quantization is investigated. Keywords: first stage of inflation, dark energy, quantum birth of the Universe.
INTRODUCTION In recent years, the number of works on quantum cosmology has increased, and the quantum birth of expanding isotropic Universes – closed, open, and flat – continues to be investigated [1–4]. Along with this, the wave function for a homogeneous isotropic model of the Universe with an electromagnetic field, pure radiation, and a rotating liquid, whose behavior is described by the cosmological solution of Vaidya and Patel, was found by Fang and Mo [5] who concluded that cosmological states with large global rotations are improbable. Fil’chenkov and Saibatalov considered the quantum evolution of homogeneous rotating cosmological models of Gödel type with a spinor and a scalar field within the formalism of superspace quantization [6]. They showed that the De Witt equation for rotating cosmological models takes the form of the Schrödinger equation in which the role of time is played by the phase of the spinor field, and the possibility arises of correctly determining the probability of the existence of rotating models in which the initial singularity is absent. Quantum birth of the Universe with slow rotation was investigated in [7, 8], where it was established within the framework of their respective approaches that rotation can both decrease and increase the tunneling coefficient of the Universe. Quantum birth of the Universe with arbitrary rotation was considered in [9–11]. An examination of the role of rotation in the description of the early Universe and in the quantum birth of the Universe is of urgent interest. In the present paper, we investigate the possibility of quantum birth of a model Universe with a Bianchi type IX metric.
THE BIANCHI IX MODEL In the present work, within the framework of the general theory of relativity, we have found a solution with rotation based on a Bianchi type IX metric having the form
ds 2 (dt A1 ) 2 ( B1 ) 2 C 2 ((2 ) 2 (3 ) 2 ) ,
(1)
where A, B, and C are functions that depend on time, and 1 , 2 , and 3 are 1-forms satisfying structural Bianchi type IX relations. We represent our metric in tetrad form. We employ the Lorentz tetrad with nonzero
Perm State National Research University, Perm, Russia, e-mail: [email protected]. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 147–151, June, 2020. Original article submitted January 9, 2020. 1064
1064-8887/20/6306-1064 2020 Springer Science+Business Media, LLC
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