Dynamical system analysis of interacting models

• Published in: General relativity and gravitation 2018, Vol.50 (1), p.1-11, Article 1
• Main Authors: Carneiro, S., Borges, H. A.
• Format: Article
• Language: English
• Subjects: Astronomical models; Astronomy; Astrophysics and Cosmology; Classical and Quantum Gravitation; Critical point; Dark matter; Differential Geometry; Dynamical systems; Gravity; Mathematical and Computational Physics; Physics; Physics and Astronomy; Quantum Physics; Red shift; Relativity Theory; Research Article; Spacetime; Systems analysis; Theoretical; Universe
• ISSN: 0001-7701; 1572-9532
• DOI: 10.1007/s10714-017-2322-8

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.