相关论文: On asymptotic solutions of Friedmann equations
A positive cosmological constant simplifies the asymptotics of forever expanding cosmological solutions of the Einstein equations. In this paper a general mathematical analysis on the level of formal power series is carried out for vacuum…
Assuming a Friedmann universe which evolves with a power-law scale factor, $a=t^{n}$, we analyse the phase space of the system of equations that describes a time-varying fine structure 'constant', $\alpha$, in the…
We investigate self-similar solutions which are asymptotic to the Friedmann universe at spatial infinity and contain a scalar field with potential. The potential is required to be exponential by self-similarity. It is found that there are…
Evolution of the scale factor a(t) in Friedmann models (those with zero pressure and a constant cosmological term Lambda) is well understood, and elegantly summarized in the review of Felten and Isaacman [Rev. Mod. Phys. 58, 689 (1986)].…
The Einstein equations of general relativity reduce, when the spacetime metric is of the Friedmann--Lemaitre--Robertson--Walker type governing an isotropic and homogeneous universe, to the Friedmann equations, which is a set of nonlinear…
We reconstruct $F(\mathcal{G})$ gravity theory with an exponential scale factor to realize the bouncing behavior in the early universe and examine the asymptotic behaviour of late-time solutions in this model. We propose an approach to the…
As a Newtonian cosmological model the Vlasov-Poisson-Boltzmann system is considered, and a slightly modified Boltzmann equation, which describes the stability of an expanding universe, is derived. Asymptotic behaviour of solutions turns out…
The cosmological term is assumed to be a function of time such as $\Lambda =Ba^{-2}$ where a(t) means the scale factor of standard cosmology. Analytical solutions for radiation dominated epoch and open universe are found. For closed…
This article is focused on the asymptotic expansions, as time tends to infinity, of solutions of a system of ordinary differential equations with non-smooth nonlinear terms. The forcing function decays to zero in a very complicated but…
A new uniform asymptotic expansion for the incomplete gamma function $\Gamma(a,z)$ valid for large values of $z$ was given by the author in {\it J. Comput. Appl. Math.} {\bf 148} (2002) 323--339. This expansion contains a complementary…
The non-singular, oscillating Friedman cosmology within the framework of General Relativity is considered. The general oscillatory solution given in terms of elliptic functions and the conditions for its existence are discussed. It is shown…
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…
This paper is concerned with the asymptotic behavior of sums of terms which are a test function f evaluated at successive increments of a discretely sampled semimartingale. Typically the test function is a power function (when the power is…
If the fine structure constant $\alpha =e^2/(\hbar c)$ were to change, then a number of interpretations would be possible, attributing this change either to variations in the electron charge, the dielectric constant of the vacuum, the speed…
The asymptotic behavior of a nonlinear diffusive equation obtained in the framework of the $\kappa$-generalized statistical mechanics is studied. The analysis based on the classical Lie symmetry shows that the $\kappa$-Gaussian function is…
This paper develops further and systematically the asymptotic expansion theory that was initiated by Foias and Saut in [11]. We study the long-time dynamics of a large class of dissipative systems of nonlinear ordinary differential…
The ADM formalism together with a constant mean curvature (CMC) temporal gauge is used to derive the monotonic decay of a weak Lyapunov function of the Einstein dynamical equations in an expanding universe with a positive cosmological…
We provide a new extension of general relativity (GR) which has the remarkable property of being more constrained than GR plus a cosmological constant, having one less free parameter. This is implemented by allowing the cosmological…
We consider a cosmology in which the final stage of the Universe is neither accelerating nor decelerating, but approaches an asymptotic state where the scale factor becomes a constant value. In order to achieve this, we first bring in a…
Asymptotic expansions are derived for solutions of the parabolic cylinder and Weber differential equations. In addition the inhomogeneous versions of the equations are considered, for the case of polynomial forcing terms. The expansions…