# Dynamical system analysis at background and perturbation levels: Quintessence in severe disadvantage comparing to $\Lambda$CDM

## TL;DR

This study compares the stability and physical viability of $ ext{Λ}$CDM and quintessence cosmologies by analyzing background and perturbation equations, revealing significant disadvantages of quintessence due to instabilities and unphysical behaviors.

## Contribution

First dynamical system analysis of both background and perturbation equations for $ ext{Λ}$CDM and quintessence with exponential potential, highlighting stability differences.

## Key findings

- Perturbations do not affect $ ext{Λ}$CDM stability, which remains consistent with observations.
- Quintessence exhibits instabilities and unphysical matter clustering when perturbations are included.
- $ ext{Λ}$CDM is more physically viable than quintessence due to stability and observational consistency.

## Abstract

We perform for the first time a dynamical system analysis of both the background and perturbation equations, of $\Lambda$CDM cosmology and quintessence scenario with an exponential potential. In the former case the perturbations do not change the stability of the late-time attractor of the background equations, and the system still results in the dark-energy dominated, de Sitter solution, having passed from the correct dark-matter era with $\gamma\approx6/11$. However, in the case of quintessence the incorporation of perturbations changes the stability and properties of the background evolution, and the only conditionally stable points present either an exponentially increasing matter clustering not favored by observations, or Laplacian instabilities, and thus not physically interesting. This result is a severe disadvantage of quintessence cosmology comparing to $\Lambda$CDM paradigm.