相关论文: A Dynamical Study of the Friedmann Equations
According to observations, in our Universe for gravitational phenomena in a Newtonian approximation the Newtonian non-modified relations are valid. The Friedmann equations of universe dynamics describe infinite number of relativistic…
According to the observations, in our expansive and isotropic relativistic Universe for the gravitational phenomena in a Newtonian approximation the Newtonian non-modified relations are valid. The Friedmann general equations of isotropic…
We start with the cosmic Friedmann equations, where we adopt a novel perspective rooted in a Lagrangian formulation grounded in Newtonian mechanics and the first law of thermodynamics. Our investigation operates under the assumption that…
In this paper we describe the evolution of the Universe in terms of the Friedmann equation, which takes into account of the composition and geometry of the Universe. The dependence of the solution on the geometry and composition for…
Active motion is a concept in complex systems theory and was successfully applied to various problems in nonlinear dynamics. Explicit studies for gravitational potentials were missing so far. We interpret the Friedmann equations with…
Universe evolution, as described by Friedmann's equations, is determined by source terms fixed by the choice of pressure $\times$ energy-density equations of state $p(\rho)$. The usual approach in Cosmology considers equations of state…
The Universe dynamical equations discovered by Alexander Friedmann in 1922 are simple enough to be clear for undergraduate students or even for smart senior schoolkids. The background cosmology driven by the dust-like matter and by positive…
Dynamical systems techniques are a powerful tool to analyse systems of ordinary differential equations, written in an appropriate form. For a given theory of gravity, the cosmological field equations typically lead to a system of ordinary…
It is useful to study the space of all cosmological models from a dynamical systems perspective, that is, by formulating the Einstein field equations as a dynamical system using appropriately normalized variables. We will discuss various…
The Friedmann equation is derived for a Newtonian universe. Changing mass density to energy density gives exactly the Friedmann equation of general relativity. Accounting for work done by pressure then yields the two Einstein equations that…
In this note, we discuss how possible expansion histories of the universe can be inferred in a simple way, for arbitrary energy contents. No new physical results are obtained, but the goal is rather to discuss an alternative way of writing…
The general relativistic cosmological Friedmann equations which describe how the scale factor of the universe evolves are expanded explicitly to include energy forms not usually seen. The evolution of the universe as predicted by the…
It is known that in Friedmann-Lemaitre-Robertson-Walker cosmology one has more number of dynamical equations, compared to the number of unknown variables. This fact makes some equations redundant. The situation becomes complicated because…
We investigate a class of cosmological solutions of Einstein's field equations in higher dimensions with a cosmological constant and an ideal fluid matter distribution as a source. We discuss the dynamical evolution of the universe subject…
It has been known for some time that the cosmological Friedmann equation deduced from General Relativity can be also obtained within the Newtonian framework under certain assumptions. We use this result together with quantum corrections to…
Based on the Newtonian mechanics, in this article, we present a heuristic derivation of the Friedmann equations, providing an intuitive foundation for these fundamental relations in cosmology. Additionally, using the first law of…
The role of global topology in the dynamics of the Universe is poorly understood. Along with observational programmes for determining the topology of the Universe, some small theoretical steps have recently been made. Heuristic…
Complex systems throughout Nature display structures and functions that are built and maintained, at least in part, by optimal energies flowing through them--not specific, ideal values, rather ranges in energy rate density below which…
We consider the evolution of a flat Friedmann-Roberstson-Walker Universe in a higher derivative theories, including $\alpha R^{2}$ terms to the Einstein-Hilbert action in the presence of a variable gravitational and cosmological constants.…
We investigate cosmological dynamics based on $f(R)$ gravity in the Palatini formulation. In this study we use the dynamical system methods. We show that the evolution of the Friedmann equation reduces to the form of the piece-wise smooth…