Wheeler–DeWitt equation and Lie symmetries in Bianchi scalar-field cosmology

Paliathanasis, Andronikos; Karpathopoulos, Leonidas; Wojnar, Aneta; Capozziello, Salvatore

doi:10.1140/epjc/s10052-016-4087-8

Cited by 14 publications

(14 citation statements)

References 60 publications

(90 reference statements)

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“…This is the second paper of the "Averaging generalized scalar field cosmologies" program that was initiated in reference [20]. This program consists in using asymptotic methods and averaging theory to obtain relevant information about solution's space of scalar field cosmologies in presence of a matter fluid with EoS with barotropic index γ minimally coupled to a scalar field with generalized harmonic potential (1).…”

Section: Discussionmentioning

confidence: 99%

“…Potential (1) or (2) is related but not equal to the monodromy potential of [56] used in the context of loop-quantum gravity, which is a particular case of the general monodromy potential [57]. In references [17][18][19] it was proved that the potential of [56,57]…”

Section: The Generalized Harmonic Potentialmentioning

confidence: 99%

“…Mathematical methods have been widely used in cosmology. For example, in reference [1] the method of Lie symmetries was applied to Wheeler-De Witt equation in Bianchi class A cosmologies for minimally coupled scalar field gravity a e-mail: genly.leon@ucn.cl (corresponding author) b e-mail: sebastian.cuellar01@ucn.cl c e-mail: esteban.gonzalezb@usach.cl d e-mail: samuel.lepe@pucv.cl e e-mail: claudio.ramirez@ce.ucn.cl f e-mail: alfredo.millano@alumnos.ucn.cl and hybrid gravity in general relativity (GR). Several invariant solutions were determined and classified.…”

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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Section: Discussionmentioning

confidence: 99%

Section: The Generalized Harmonic Potentialmentioning

confidence: 99%

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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“…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. Using these symmetries several invariant solutions were determined and classified according to the form of scalar field potential.…”

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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“…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). Several invariant solutions were determined and classified according to the form of the scalar-field potential by means of these symmetries.…”

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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Wheeler–DeWitt equation and Lie symmetries in Bianchi scalar-field cosmology

Cited by 14 publications

References 60 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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