Quantum singularities in FRW universe revisited

TL;DR

This paper investigates quantum effects in a flat FRW universe, showing that quantum cosmology can remove classical singularities and alter energy conditions, with results depending on the interpretation and wave packet choice.

Contribution

It provides a detailed analysis of quantum cosmology in the FRW model, demonstrating singularity removal and the impact of wave packet normalization on the universe's quantum behavior.

Findings

Quantum expectation values remove classical singularities.

Energy conditions are violated in the quantum regime.

Singularity can reappear with non-normalizable wave packets.

Abstract

The components of the Riemann tensor in the tetrad basis are quantized and, through the Einstein equation, we find the local expectation value in the ontological interpretation of quantum mechanics of the energy density and pressure of a perfect fluid with equation of state $p=\frac{1}{3}\rho$ in the flat Friedmann-Robertson-Walker quantum cosmological model. The quantum behavior of the equation of state and energy conditions are then studied and it is shown that the later is violated since the singularity is removed with the introduction of quantum cosmology, but in the classical limit both the equation of state and the energy conditions behave as in the classical model. We also calculate the expectation value of the scale factor for several wave packets in the many-worlds interpretation in order to show the independence of the non singular character of the quantum cosmological model with respect to the wave packet representing the wave function of the Universe. It is also shown that, with the introduction of non-normalizable wave packets, solutions of the Wheeler-DeWitt equation, the singular character of the scale factor, can be recovered in the ontological interpretation.