An Early Universe Model with Stiff Matter and a Cosmological Constant

TL;DR

This paper explores a quantum cosmology model with stiff matter and a negative cosmological constant, demonstrating a non-singular bouncing universe at both classical and quantum levels through the Wheeler-DeWitt equation.

Contribution

It introduces a quantum cosmology model with negative energy density stiff matter and analyzes its bounded states and bouncing behavior.

Findings

The model has a discrete energy spectrum with negative eigenvalues.

The expectation value of the scale factor oscillates, avoiding initial singularity.

Quantum analysis confirms a non-singular bouncing universe.

Abstract

In the present work, we study the quantum cosmology description of a Friedmann-Robertson-Walker model in the presence of a stiff matter perfect fluid and a negative cosmological constant. We work in the Schutz's variational formalism and the spatial sections have constant negative curvature. We quantize the model and obtain the appropriate Wheeler-DeWitt equation. In this model the states are bounded therefore we compute the discrete energy spectrum and the corresponding eigenfunctions. In the present work, we consider only the negative eigenvalues and their corresponding eigenfunctions. This choice implies that the energy density of the perfect fluid is negative. A stiff matter perfect fluid with this property produces a model with a bouncing solution, at the classical level, free from an initial singularity. After that, we use the eigenfunctions in order to construct wave packets and evaluate the time-dependent expectation value of the scale factor. We find that it oscillates between maximum and minimum values. Since the expectation value of the scale factor never vanishes, we confirm that this model is free from an initial singularity, also, at the quantum level.