Constructing the CKVs of Bianchi III and V spacetimes

Mitsopoulos, Antonios; Tsamparlis, Michael; Paliathanasis, Andronikos

doi:10.1142/s0217732319503267

Cited by 8 publications

(8 citation statements)

References 38 publications

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“…For other applications of Kasner universe and Bianchi I spacetimes in gravitational physics see [188][189][190][191][192][193][194][195] and references therein. In [196] the conformal algebra of Bianchi III and Bianchi V spacetimes which admit a proper conformal Killing vector were studied. In [197] method of Lie symmetries was applied for the Wheeler-De Witt equation in Bianchi class A cosmologies for minimally coupled scalar field gravity and hybrid gravity in GR.…”

Section: Spatially Homogeneous Scalar Field Cosmologiesmentioning

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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Section: Spatially Homogeneous Scalar Field Cosmologiesmentioning

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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“…The conformal algebra of Bianchi III and Bianchi V spacetimes, which admits a proper conformal Killing vector, was studied in [48]. In [49] the method of Lie symmetries was applied for Wheeler-De Witt equation in Bianchi Class A cosmologies for minimally coupled scalar-field gravity and Hybrid Gravity in General Relativity (GR).…”

Section: Introductionmentioning

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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“…Theorem 3 Let be defined the functions Ω, Σ, Ωk , Φ, and D, satisfying the time-averaged equations (40), ( 41), ( 42), ( 43) and (44). Then, there exists functions g 1 , g 2 , g 3 and g 4 , such that if…”

Section: Kantowski-sachsmentioning

confidence: 99%

“…The conformal algebra of Bianchi III and Bianchi V spacetimes which admit a proper conformal Killing vector was studied in [44]. In [45] the method of Lie symmetries was applied for the Wheeler-De Witt equation in Bianchi Class A cosmologies for minimally coupled scalar field gravity and Hybrid Gravity in General Relativity (GR).…”

mentioning

confidence: 99%

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

León¹,

González²,

Lepe³

et al. 2021

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Scalar field cosmologies with a generalized harmonic potential and a background matter given by a barotropic Equation of State (EoS) are investigated for Kantowski-Sachs metric and closed Friedmann-Lemaître-Robertson-Walker (FLRW) metrics. Using methods from the Theory of Averaging of Nonlinear Dynamical Systems and numerical simulations it is proved that the full equations of the time dependent system and their corresponding time-averaged versions have the same late-time dynamics. Therefore, the simplest timeaveraged system determines the future asymptotic of the full system. In particular, for Kantowski-Sachs metric the late-time attractors of the full and time-averaged systems are: two anisotropic contracting solutions for 0 ≤ γ < 2: a non-Flat LRS Kasner Bianchi I and a Taub (flat LRS Kasner) and the flat matter dominated FLRW universe if 0 ≤ γ ≤ 2 3 (mimicking de Sitter, quintessence or zero acceleration solutions). For closed FLRW metric the late-time attractors are: the flat Friedman Einstein-de-Sitter solution for 0 < γ < 1, the flat matter dominated FLRW universe for 0 ≤ γ ≤ 2 3 (mimicking de Sitter, quintessence or zero acceleration solutions), and a matter dominated contracting isotropic solution for 1 < γ < 2. With this approach the oscillations entering the system through Klein-Gordon equation can be controlled and smoothed out as a relevant time-dependent perturbative parameter goes monotonically to zero for a finite time t < t * . The region where the perturbation parameter changes its monotony to monotonic increasing is analyzed by a discrete symmetry and by using proper variables that brings infinity to a finite interval.

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Constructing the CKVs of Bianchi III and V spacetimes

Cited by 8 publications

References 38 publications

Averaging generalized scalar field cosmologies I: locally rotationally symmetric Bianchi III and open 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

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

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