# Bianchi models with a free massless scalar field: invariant sets and higher symmetries

## TL;DR

This paper analyzes the structure of Bianchi cosmological models with a free massless scalar field, classifying invariant sets and higher-symmetry models, and determining initial data dimensions for each case.

## Contribution

It provides a detailed classification of Bianchi models with a scalar field, including invariant sets, higher-symmetry models, and initial data dimensions, enhancing understanding of their geometric and physical properties.

## Key findings

- Invariant sets correspond to specific Bianchi types and matter contents.
- Higher-symmetry models include all locally rotationally symmetric and FLRW models.
- The dimension of initial data space is explicitly determined for each model.

## Abstract

We scrutinize the overall structure of the space of cosmological models of Bianchi type I-VII$_h$ that contain a free massless scalar field, with a spatially homogeneous gradient $\nabla_\mu \varphi$ that generally breaks isotropy, in addition to a standard perfect fluid. Specifically, state space is written as a union of disjoint invariant sets, each corresponding to a particular cosmological model that is classified with respect to the Bianchi type and the matter content. Subsets corresponding to higher-symmetry models, including all locally rotationally symmetric models and FLRW models, and models with a shear-free normal congruence, are also derived and classified. For each model the dimension ($d$) of the space of initial data is given, after fixing the orientation of the orthonormal frame uniquely relative to matter anisotropies and geometrical anisotropies.