# Oscillating Towards the de Sitter Universe

## TL;DR

This paper investigates conditions under which flat FLRW cosmological models with scalar fields and matter exhibit oscillations, showing they tend to decay towards a de Sitter universe, suggesting multiple oscillations before inflation.

## Contribution

It characterizes oscillatory behavior in flat FLRW models with scalar fields and matter, revealing decay towards de Sitter space and potential multiple oscillations before inflation.

## Key findings

- Oscillations occur in models with positive cosmological constant and matter.
- Oscillations decay over time, approaching de Sitter equilibrium.
- Models can oscillate multiple times before inflation.

## Abstract

In this paper, we consider spatially flat FLRW cosmological models in two contexts in an attempt to derive a set of conditions that characterize when such models exhibit oscillatory behaviour. In the first case, we consider a spatially flat FLRW model with only a minimally-coupled scalar field, described by a nonnegative scalar field potential. In the second case, we extended this model to include barotropic matter. We show that for the case of a positive cosmological constant, spatial flatness, and barotropic matter, oscillatory solutions are certainly possible. However, these solutions do not oscillate indefinitely, they decay over time. Interestingly, it is shown that all such solutions oscillate and decay towards the de Sitter equilibrium point, which represents an inflationary epoch in such models. This implies that for certain families of scalar field potentials, the universe may have undergone several oscillations \emph{before} entering an inflationary epoch.