Dynamics of two Einstein–Friedmann cosmological models

Inna Basak; Jaume Llibre

doi:10.1140/epjp/s13360-020-01000-8

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2024 Impact factor 2.9

EPJ PLUS - Condensed Matter and Complex Systems

Eur. Phys. J. Plus (2021) 136: 8
https://doi.org/10.1140/epjp/s13360-020-01000-8

Regular Article

Dynamics of two Einstein–Friedmann cosmological models

Inna Basak and Jaume Llibre^b

Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra, Barcelona, Catalonia, Spain

^b jllibre@mat.uab.cat

Received: 25 June 2020
Accepted: 8 December 2020
Published online: 2 January 2021

Abstract

We describe completely the dynamics of the two Einstein–Friedmann cosmological models, which can be characterized by the Hamiltonians $\begin{matrix} H = \frac{1}{2} (p_{y}^{2} - p_{x}^{2}) + e^{2 x} V (y), \end{matrix}$ $\begin{aligned} H = \frac{1}{2} (p_{y}^2 - p_{x}^2) + e^{2 x} V(y), \end{aligned}$ with the cosmological potentials $V (y) = e^{λ y}$ $V(y)=e^{\lambda y}$ , or $V (y) = (a + b y) e^{y}$ $V(y)=(a+by)e^{y}$ with $λ a b \neq 0$ $\lambda a b\ne 0$ .