Simplicial minisuperspace models in the presence of a scalar field

TL;DR

This paper extends simplicial minisuperspace models to include a scalar field, analyzing their classical solutions and wavefunctions, and demonstrating that they predict Lorentzian oscillatory behavior in the late universe.

Contribution

It introduces a generalized class of models with scalar fields, studies their classical extrema, and constructs convergent wavefunctions supporting Lorentzian late-time behavior.

Findings

Wavefunctions predict Lorentzian oscillations in the late universe

Classical extrema are identified through analytic properties of the action

Steepest descent contours yield convergent, semiclassical wavefunctions

Abstract

We generalize simplicial minisuperspace models associated with restricting the topology of the universe to be that of a cone over a closed connected combinatorial $3-$manifold by considering the presence of a massive scalar field. By restricting all the interior edge lengths and all the boundary edge lengths to be equivalent and the scalar field to be homogenous on the $3-$space, we obtain a family of two dimensional models that include some of the most relevant triangulations of the spatial universe. After studying the analytic properties of the action in the space of complex edge lengths we determine its classical extrema. We then obtain steepest descents contours of constant imaginary action passing through Lorentzian classical geometries yielding a convergent wavefunction of the universe, dominated by the contributions coming from these extrema. By considering these contours we justify semiclassical approximations based on those classical solutions, clearly predicting classical spacetime in the late universe. These wavefunctions are then evaluated numerically. For all of the models examined we find wavefunctions predicting Lorentzian oscillatory behaviour in the late universe.