# Noether symmetries and stability of ideal gas solution in Galileon Cosmology

## TL;DR

This paper uses Noether's theorem to find conservation laws in generalized Galileon cosmology, enabling the construction and stability analysis of specific power-law solutions in an expanding universe.

## Contribution

It introduces a method to identify conservation laws in complex Galileon models and applies differential invariants to derive and analyze power-law solutions.

## Key findings

- Existence of nontrivial conservation laws indicating integrability.
- Construction of special power-law solutions.
- Stability analysis of these solutions.

## Abstract

A class of generalized Galileon cosmological models, which can be described by a point-like Lagrangian, is considered in order to utilize Noether's Theorem to determine conservation laws for the field equations. In the Friedmann-Lema\^itre-Robertson-Walker universe, the existence of a nontrivial conservation law indicates the integrability of the field equations. Due to the complexity of the latter, we apply the differential invariants approach in order to construct special power-law solutions and study their stability.