Resonant structure of space-time of early universe

Abstract

A new fully quantum method describing penetration of packet from internal well outside with its tunneling through the barrier of arbitrary shape used in problems of quantum cosmology, is presented. The method allows to determine amplitudes of wave function, penetrability $T_{\mathrm{bar}}$ and reflection $R_{\mathrm{bar}}$ relatively the barrier (accuracy of the method: $|T_{\mathrm{bar}}+R_{\mathrm{bar}}-1|<1\cdot 10^{-15}$), coefficient of penetration (i.e. probability of the packet to penetrate from the internal well outside with its tunneling), coefficient of oscillations (describing oscillating behavior of the packet inside the internal well). Using the method, evolution of universe in the closed Friedmann--Robertson--Walker model with quantization in presence of positive cosmological constant, radiation and component of generalize Chaplygin gas is studied. It is established (for the first time): (1) oscillating dependence of the penetrability on localization of start of the packet; (2) presence of resonant values of energy of radiation $E_{\mathrm{rad}}$, at which the coefficient of penetration increases strongly. From analysis of these results it follows: (1) necessity to introduce initial condition into both non-stationary, and stationary quantum models; (2) presence of some definite values for the scale factor $a$, where start of expansion of universe is the most probable; (3) during expansion of universe in the initial stage its radius is changed not continuously, but passes consequently through definite discrete values and tends to continuous spectrum in latter time.

18 pages, 14 figures, 4 tables

References in corpus (5)

• On the generalised Chaplygin gas: worse than a big rip or quieter than a sudden singularity?
• Observational constraint on generalized Chaplygin gas model
• The method of multiple internal reflections in a description of tunneling evolution of nonrelativistic particles and photons
• Wave function of the Universe in the early stage of its evolution
• Iso-spectral potential and inflationary quantum cosmology

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• Quantum design in study of pycnonuclear reactions in compact stars and new quasibound states
• Quantum dynamics of evolution of flat universe in the first stage
• Quantum dynamics of early Universe