Global dynamics and evolution for the Szekeres system with nonzero cosmological constant term
Abstract
The Szekeres system with cosmological constant term describes the evolution of the kinematic quantities for Einstein field equations in $\mathbb{R}^4$. In this study, we investigate the behavior of trajectories in the presence of cosmological constant. It has been shown that the Szekeres system is a Hamiltonian dynamical system. It admits at least two conservation laws, $h$ and $I_{0}$ which indicate the integrability of the Hamiltonian system. We solve the HamiltonJacobi equation, and we reduce the Szekeres system from $\mathbb{R}^4$ to an equivalent system defined in $\mathbb{R}^2$. Global dynamics are studied where we find that there exists an attractor in the finite regime only for positive valued cosmological constant and $I_0<2.08$. Otherwise, trajectories reach infinity. For $I_ {0}>0$ the origin of trajectories in $\mathbb{R}^2$ is also at infinity. Finally, we investigate the evolution of physical properties by using dimensionless variables different from that of Hubblenormalization conducing to a dynamical system in $\mathbb{R}^5$. We see that the attractor at the finite regime in $\mathbb{R}^5$ is related with the de Sitter universe for a positive cosmological constant.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.06904
 Bibcode:
 2021arXiv210906904P
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 45 pages, 20 compound figures, 1 table