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

TL;DR

This paper introduces a fully quantum method to accurately calculate penetrability and reflection coefficients in a quantum cosmological model, accounting for wave interference and non-local barrier effects, aligning well with semiclassical results.

Contribution

A novel quantum approach for determining tunneling and reflection coefficients in the FRW cosmological model, incorporating wave interference and non-local barrier effects.

Findings

Tunneling probability closely matches semiclassical results.

First calculation of reflection coefficient in this context.

Method applicable to models with arbitrary barrier shapes.

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.