Scalar Field Cosmological Models With Hard Potential Walls

TL;DR

This paper studies scalar field cosmological models with steep potential walls, revealing oscillatory behavior near singularities caused by the scalar field's interaction with the potential walls.

Contribution

It introduces a simple model with an exponential steep potential well to analyze the complex oscillatory behavior near singularities in scalar field cosmologies.

Findings

Solutions exhibit non-trivial oscillations near singularities.

Oscillations are due to the scalar field's inability to pass through steep potential walls.

Behavior provides insight into early universe dynamics with hard potential walls.

Abstract

The global behavior of scalar field cosmological models with very hard potential walls is investigated via the simple example of an exponentially steep potential well. It is found that the solutions exhibit a non-trivial oscillatory behavior in the approach to an initial space-time singularity. This behavior can be interpreted as being due to the inability of the scalar field to negotiate the walls of the steep potential well.