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

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

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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 $$\begin{array}{c}\hfill H=\frac{1}{2}(p_y^2-p_x^2)+e^{2x}V(y),\end{array}$$with the cosmological potentials $V(y)=e^{\lambda y}$, or $V(y)=(a+by)e^y$ with $\lambda ab\ne 0$.