A fully quantum method of determination of penetrability and reflection coefficients in quantum FRW model with radiation

Abstract

In the paper the closed Friedmann--Robertson--Walker model with quantization in the presence of the positive cosmological constant and radiation is studied. For analysis of tunneling probability for birth of an asymptotically deSitter, inflationary Universe as a function of the radiation energy a new definition of a "free" wave propagating inside strong fields is proposed. On such a basis, tunneling boundary condition is corrected, penetrability and reflection concerning to the barrier are calculated in fully quantum stationary approach. For the first time non-zero interference between the incident and reflected waves has been taken into account which turns out to play important role inside cosmological potentials and could be explained by non-locality of barriers in quantum mechanics. Inside whole region of energy of radiation the tunneling probability for the birth of the inflationary Universe is found to be close to its value obtained in semiclassical approach. The reflection from the barrier is determined for the first time (which is essentially differs on 1 at the energy of radiation close to the barrier height). The proposed method could be easily generalized on the cosmological models with the barriers of arbitrary shape, that has been demonstrated for the FRW-model with included Chaplygin gas. Result is stable for variations of the studied barriers, accuracy are found to be 11--18 digits for all coefficients and energies below the barrier height.

28 pages, 7 figures (20 files in eps format), 4 tables

References in corpus (7)

• Improved WKB analysis of cosmological perturbations
• Improved WKB analysis of Slow-Roll Inflation
• Tunneling probability for the birth of an asymptotically DeSitter universe
• The method of multiple internal reflections in a description of tunneling evolution of nonrelativistic particles and photons
• Method of multiple internal reflections in description of tunneling evolution through barriers
• Wave function of the Universe in the early stage of its evolution
• Semiclassical Approximations to Cosmological Perturbations

Cited by in corpus (5)

• Quantum design using a multiple internal reflections method in a study of fusion processes in the capture of alpha-particles by nuclei
• Resonant structure of space-time of early universe
• Quantum dynamics of evolution of flat universe in the first stage
• Quantum dynamics of early Universe
• Quantum method of determination of penetrability in FRW model with radiation