Radiation-dominated quantum Friedmann models

Abstract

Radiation-filled Friedmann-Robertson-Walker universes are quantized according to the Arnowitt-Deser-Misner formalism in the conformal-time gauge. Unlike previous treatments of this problem, here both closed and open models are studied, only square-integrable wave functions are allowed, and the boundary conditions to ensure self-adjointness of the Hamiltonian operator are consistent with the space of admissible wave functions. It turns out that the tunneling boundary condition on the universal wave function is in conflict with selfadjointness of the Hamiltonian. The evolution of wave packets obeying different boundary conditions is studied and it is generally proven that all models are nonsingular. Given an initial condition on the probability density under which the classical regime prevails, it is found that a closed universe is certain to have an infinite radius, a density parameter Ω = 1 becoming a prediction of the theory. Quantum stationary geometries are shown to exist for the closed universe model, but oscillating coherent states are forbidden by the boundary conditions that enforce self-adjointness of the Hamiltonian operator.

Notes on the quantization of FRW model in the presence of a cosmological constant and radiation

“…Another way by which one may compute the wave-function of the Universe is by directly solving the Wheeler-DeWitt equation [1]. The wave-function of the Universe for some important models have been computed using this approach [5][6][7][8][9][10].…”

“…Another way by which one may compute the wave-function of the Universe is by directly solving the Wheeler-DeWitt equation [1]. The wave-function of the Universe for some important models have been computed using this approach [5][6][7][8][9][10].Several important theoretical results and predictions in quantum cosmology have been obtained with a negative cosmological constant [11], [12] and [3]. Besides that, we think it is important to understand more about such models which represent bound Universes (analogous to uni-dimensional atoms, in the present situation).…”

Tomographic entropy and cosmology

“…As the simplest example of the suggested transition probability picture, we considered the minisuperspace model for which classical and quantum evolution is described by the harmonic vibrations in conformal time [21], [23], [27], [24]. The specific property of this minisuperspace model is that the tomographic propagators for both classical and quantum universe tomograms coincide.…”

“…An alternative way to describe cosmology with a cosmological fluid, with Λ = 0, was introduced firstly by Lemos [21], Faraoni [23] and also in [2] and [24].…”

“…In order to illustrate the idea we will use the same simple example of the universe description by means of the minisuperspace discussed, e.g., in [7], [21] . In these minisuperspaces the quantum cosmological dynamics in operative form is reduced to the dynamics of formal quantum systems described by Hamiltonians of the types of oscillator, free motion and free falling particles.…”