Perfect fluid Friedmann-Robertson-Walker quantum cosmological models for an arbitrary barotropic equation of state p = αρ are constructed using Schutz's variational formalism. In this approach the notion of time can be recovered. By superposition of stationary states, finite-norm wave-packet solutions to the Wheeler-DeWitt equation are found. The behaviour of the scale factor is studied by applying the many-worlds and the ontological interpretations of quantum mechanics. Singularity-free models are obtained for α < 1. Accelerated expansion at present requires −

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.

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In the present work, we quantize three Friedmann-Robertson-Walker models in the presence of a negative cosmological constant and radiation. The models differ from each other by the constant curvature of the spatial sections, which may be positive, negative or zero.They give rise to Wheeler-DeWitt equations for the scale factor which have the form of the Schrödinger equation for the quartic anharmonic oscillator. We find their eigenvalues and eigenfunctions by using a method first developed by Chhajlany and Malnev. After that, we use the eigenfunctions in order to construct wave packets for each case and evaluate the time-dependent expected value of the scale factors. We find for all of them that the expected values of the scale factors oscillate between maximum and minimum values. Since the expectation values of the scale factors never vanish, we conclude that these models do not have singularities.

It is known that certain quantum cosmological models present quantum behavior for large scale factors. Since quantization can suppress past singularities, it is natural to inquire whether quantum effects can prevent future singularities. To this end, a Friedmann-Robertson-Walker quantum cosmological model dominated by a phantom energy fluid is investigated. The classical model displays accelerated expansion ending in a Big Rip. The quantization is performed in three different ways, which turn out to lead to the same result, namely there is a possibility that quantum gravitational effects could not remove the Big Rip.Comment: Ref. [21] added, abstract slightly change