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Register a new userGlobal dynamics of Yang-Mills field and perfect-fluid Robertson-Walker cosmologies
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We apply a new global dynamical systems formulation to flat Robertson-Walker cosmologies with a massless and massive Yang-Mills field and a perfect-fluid with linear equation of state as the matter sources. This allows us to give proofs concerning the global dynamics of the models including asymptotic source-dominance towards the past and future time directions. For the pure massless Yang-Mills field, we also contextualize well-known explicit solutions in a global (compact) state space picture.
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Scalar field cosmologies with a generalized harmonic potential and matter with energy density $rho_m$, pressure $p_m$, and barotropic equation of state (EoS) $p_m=(gamma-1)rho_m, ; gammain[0,2]$ in Kantowski-Sachs (KS) and closed Friedmann--Lema^itre--Robertson--Walker (FLRW) metrics are investigated. We use methods from non--linear dynamical systems theory and averaging theory considering a time--dependent perturbation function $D$. We define a regular dynamical system over a compact phase space, obtaining global results. That is, for KS metric the global late--time attractors of full and time--averaged systems are two anisotropic contracting solutions, which are non--flat locally rotationally symmetric (LRS) Kasner and Taub (flat LRS Kasner) for $0leq gamma leq 2$, and flat FLRW matter--dominated universe if $0leq gamma leq frac{2}{3}$. For closed FLRW metric late--time attractors of full and averaged systems are a flat matter--dominated FLRW universe for $0leq gamma leq frac{2}{3}$ as in KS and Einstein-de Sitter solution for $0leqgamma<1$. Therefore, time--averaged system determines future asymptotics of full system. Also, oscillations entering the system through Klein-Gordon (KG) equation can be controlled and smoothed out when $D$ goes monotonically to zero, and incidentally for the whole $D$-range for KS and for closed FLRW (if $0leq gamma< 1$) too. However, for $gammageq 1$ closed FLRW solutions of the full system depart from the solutions of the averaged system as $D$ is large. Our results are supported by numerical simulations.
In a recent paper [arXiv:1206.4916] by T. Padmanabhan, it was argued that our universe provides an ideal setup to stress the issue that cosmic space is emergent as cosmic time progresses and that the expansion of the universe is due to the difference between the number of degrees of freedom on a holographic surface and the one in the emerged bulk. In this note following this proposal we obtain the Friedmann equation of a higher dimensional Friedmann-Robertson-Walker universe. By properly modifying the volume increase and the number of degrees of freedom on the holographic surface from the entropy formulas of black hole in the Gauss-Bonnet gravity and more general Lovelock gravity, we also get corresponding dynamical equations of the universe in those gravity theories.
Scalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic Equation of State (EoS) with barotropic index $gamma$ for Locally Rotationally Symmetric (LRS) Bianchi III metric and open Friedmann-Lema^itre-Robertson-Walker (FLRW) metric are investigated. Methods from the theory of averaging of nonlinear dynamical systems are used to prove that time-dependent systems and their corresponding time-averag
Scalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic Equation of State (EoS) with barotropic index $gamma$ for the Locally Rotationally Symmetric (LRS) Bianchi I and flat Friedmann-Lema^itre-Robertson-Walker (FLRW) metrics are investigated. Methods from the theory of averaging of nonlinear dynamical systems are used to prove that time-dependent systems and their corresponding time-averag
It is shown that only the maximally-symmetric spacetimes can be expressed in both the Robertson-Walker form and in static form - there are no other static forms of the Robertson-Walker spacetimes. All possible static forms of the metric of the maximally-symmetric spacetimes are presented as a table. The findings are generalized to apply to functionally more general spacetimes: it is shown that the maximally symmetric spacetimes are also the only spacetimes that can be written in both orthogonal-time isotropic form and in static form.
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