A fully quantum model of Big Bang

TL;DR

This paper develops a fully quantum model of the Big Bang within a closed FRW universe, introducing a new wave propagation definition, calculating tunneling probabilities, and accounting for wave interference effects, aligning with semiclassical results.

Contribution

It presents a novel quantum approach to cosmological tunneling, including interference effects, and extends the method to models with arbitrary potential barriers.

Findings

Tunneling probability closely matches semiclassical results.

First calculation of reflection coefficient in quantum cosmology.

Method applicable to models with arbitrary potential barriers.

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.