# Scalar Fields and the FLRW Singularity

## TL;DR

This paper explores the behavior of multiple scalar fields in flat FLRW cosmology, revealing that the matter system remains deterministic at the singularity and involves a parity inversion leading to a non-orientable spacetime surface.

## Contribution

It introduces a relational autonomous system for scalar fields in FLRW cosmology that remains deterministic at the singularity and describes a parity inversion and non-orientability of spacetime.

## Key findings

- The matter dynamics form an autonomous system at the singularity.
- The singularity corresponds to a parity inversion.
- The spacetime manifold becomes non-orientable at the singularity.

## Abstract

The dynamics of multiple scalar fields on a flat FLRW spacetime can be described entirely as a relational system in terms of the matter alone. The matter dynamics is an autonomous system from which the geometrical dynamics can be inferred, and this autonomous system remains deterministic at the point corresponding to the singularity of the cosmology. We show the continuation of this system corresponds to a parity inversion at the singularity, and that the singularity itself is a surface on which the space-time manifold becomes non-orientable.