# Dynamical system analysis of interacting models

## TL;DR

This paper analyzes a cosmological model with vacuum decay and dark matter creation using dynamical systems, showing de Sitter as a stable future state and Minkowski as unstable, with implications for structure growth.

## Contribution

It introduces a dynamical system framework for a vacuum decay model with dark matter creation, revealing stability properties and observational consistency.

## Key findings

- De Sitter spacetime is an asymptotically stable critical point.
- Minkowski spacetime is an unstable critical point.
- Matter creation effects are within current observational errors.

## Abstract

We perform a dynamical system analysis of a cosmological model with linear dependence between the vacuum density and the Hubble parameter, with constant-rate creation of dark matter. We show that the de Sitter spacetime is an asymptotically stable critical point, future limit of any expanding solution. Our analysis also shows that the Minkowski spacetime is an unstable critical point, which eventually collapses to a singularity. In this way, such a prescription for the vacuum decay not only predicts the correct future de Sitter limit, but also forbids the existence of a stable Minkowski universe. We also study the effect of matter creation on the growth of structures and their peculiar velocities, showing that it is inside the current errors of redshift space distortions observations.