Global dynamics of Yang–Mills field and perfect-fluid Robertson–Walker cosmologies

Alho, Artur; Bessa, V.; Mena, Filipe C.

doi:10.1063/1.5139879

Cited by 13 publications

(37 citation statements)

References 16 publications

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“…Proceeding in analogous way as in references [24,33] but for 3 dimensional systems instead of a 1-dimensional one, we implement a local nonlinear transformation…”

Section: Bianchi I Metricmentioning

confidence: 99%

“…These methods have been applied in cosmology for example in [16][17][18][19][20][21][22][23][24] with interest in early and late-time dynamics. Some works related to Einstein-KG, Maxwell, Yang-Mills and Einstein-Vlasov systems are [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. In reference [42] LRS Bianchi type III cosmologies with a massive scalar field were studied by means of the theory of averaging of nonlinear dynamical systems.…”

Section: Introductionmentioning

confidence: 99%

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Averaging generalized scalar field cosmologies II: locally rotationally symmetric Bianchi I and flat Friedmann–Lemaître–Robertson–Walker models

et al. 2021

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Scalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic equation of state (EoS) with barotropic index $$\gamma $$ γ for the locally rotationally symmetric (LRS) Bianchi I and flat Friedmann–Lemaître–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-averaged versions have the same late-time dynamics. Therefore, the simplest time-averaged system determines the future asymptotic behavior. Depending on the values of $$\gamma $$ γ , the late-time attractors of physical interests are flat quintessence dominated FLRW universe and Einstein-de Sitter solution. With this approach, the oscillations entering the system through the Klein–Gordon (KG) equation can be controlled and smoothed out as the Hubble parameter H – acting as time-dependent perturbation parameter – tends monotonically to zero. Numerical simulations are presented as evidence of such behavior.

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“…Proceeding in analogous way as in references [24,33] but for 3 dimensional systems instead of a 1-dimensional one, we implement a local nonlinear transformation…”

Section: Bianchi I Metricmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Averaging generalized scalar field cosmologies II: locally rotationally symmetric Bianchi I and flat Friedmann–Lemaître–Robertson–Walker models

et al. 2021

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“…Proceeding in analogous way as in references [128,137] we implement a local nonlinear transformation:…”

Section: Lrs Bianchi IIImentioning

confidence: 99%

“…Scalar field theories like scalar tensor theories, and many others have been exhaustively studied for example in by means of qualitative techniques of dynamical systems from [110][111][112][113][114][115][116][117][118][119][120][121][122][123][124][125][126]. Some works related to Einstein-Klein-Gordon, Maxwell, Yang-Mills, Einstein-Vlasov systems, etc., are also studied in [127][128][129][130][131][132][133][134][135][136][137][138][139][140][141][142][143][144][145]. Perturbation methods and averaging methods were used in [127,128] with interest in early and late-time dynamics.…”

Section: Introductionmentioning

confidence: 99%

Averaging generalized scalar field cosmologies I: locally rotationally symmetric Bianchi III and open Friedmann–Lemaître–Robertson–Walker models

et al. 2021

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Scalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic Equation of State (EoS) with barotropic index $$\gamma $$ γ for locally rotationally symmetric (LRS) Bianchi III metric and open Friedmann–Lemaître–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-averaged versions have the same late-time dynamics. Therefore, simple time-averaged systems determine the future asymptotic behavior. Depending on values of barotropic index $$\gamma $$ γ late-time attractors of physical interests for LRS Bianchi III metric are Bianchi III flat spacetime, matter dominated FLRW universe (mimicking de Sitter, quintessence or zero acceleration solutions) and matter-curvature scaling solution. For open FLRW metric late-time attractors are a matter dominated FLRW universe and Milne solution. With this approach, oscillations entering nonlinear system through Klein–Gordon (KG) equation can be controlled and smoothed out as the Hubble factor H – acting as a time-dependent perturbation parameter – tends monotonically to zero. Numerical simulations are presented as evidence of such behaviour.

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“…Proceeding in an analogous way as in references [103,104] we implement a local nonlinear transformation…”

Section: The Fractional Energy Density Of Mattermentioning

confidence: 99%

Averaging generalized scalar-field cosmologies III: Kantowski–Sachs and closed Friedmann–Lemaître–Robertson–Walker models

et al. 2021

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Scalar-field cosmologies with a generalized harmonic potential and matter with energy density $$\rho _m$$ ρ m , pressure $$p_m$$ p m , and barotropic equation of state (EoS) $$p_m=(\gamma -1)\rho _m, \; \gamma \in [0,2]$$ p m = ( γ - 1 ) ρ m , γ ∈ [ 0 , 2 ] in Kantowski–Sachs (KS) and closed Friedmann–Lemaître–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 $$0\le \gamma \le 2$$ 0 ≤ γ ≤ 2 , and flat FLRW matter-dominated universe if $$0\le \gamma \le \frac{2}{3}$$ 0 ≤ γ ≤ 2 3 . For closed FLRW metric late-time attractors of full and averaged systems are a flat matter-dominated FLRW universe for $$0\le \gamma \le \frac{2}{3}$$ 0 ≤ γ ≤ 2 3 as in KS and Einstein–de Sitter solution for $$0\le \gamma <1$$ 0 ≤ γ < 1 . Therefore, a time-averaged system determines future asymptotics of the 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 closed FLRW (if $$0\le \gamma < 1$$ 0 ≤ γ < 1 ) too. However, for $$\gamma \ge 1$$ γ ≥ 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.

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Global dynamics of Yang–Mills field and perfect-fluid Robertson–Walker cosmologies

Cited by 13 publications

References 16 publications

Averaging generalized scalar field cosmologies II: locally rotationally symmetric Bianchi I and flat Friedmann–Lemaître–Robertson–Walker models

Averaging generalized scalar field cosmologies II: locally rotationally symmetric Bianchi I and flat Friedmann–Lemaître–Robertson–Walker models

Averaging generalized scalar field cosmologies I: locally rotationally symmetric Bianchi III and open Friedmann–Lemaître–Robertson–Walker models

Averaging generalized scalar-field cosmologies III: Kantowski–Sachs and closed Friedmann–Lemaître–Robertson–Walker models

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