The Kantowski-Sachs Quantum Model with Stiff Matter Fluid

Alvarenga, F. G.; Fracalossi, R.; Freitas, R. C.; Gonçalves, S. V. B.

doi:10.1007/s13538-018-0575-7

Cited by 4 publications

(5 citation statements)

References 39 publications

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“…Using similar variables as in Eqs. (92) with Σ = 0 and replacing the normalization factor D = H 2 + 3 R 6 , where 3 R denotes the 3-Ricci curvature of spatial surfaces calculated in (86) by Eq. ( 91), we obtain the system…”

Section: Flrw Metric With Positive Curvaturementioning

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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Section: Flrw Metric With Positive Curvaturementioning

confidence: 99%

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

et al. 2021

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“…and modified gravity f (R) [22,23,24,25,26,27]. The Schutz's formalism is used even with success in anisotropic quantum cosmology [28,29,30,31,32,33,34], bouncing cosmologies [35,36,37] or very recently on Brans-Dicke theory and scalar-tensor theories [38,39,40,41].…”

Section: The Schutz's Formalism In Quantum Cosmologymentioning

confidence: 99%

“…Different cosmological scenarios can be studied by varying the fluid considered by choosing different values of γ [19,20,21], models with two perfect fluids, exotic matter and modified gravity f (R) [22,23,24,25,26,27]. The Schutz's formalism is used even with success in anisotropic quantum cosmology [28,29,30,31,32,33,34], bouncing cosmologies [35,36,37] or very recently on Brans-Dicke theory and scalar-tensor theories [38,39,40,41].…”

Section: The Schutz's Formalism In Quantum Cosmologymentioning

confidence: 99%

Dynamics of a Perfect Fluid Through Velocity Potentials with Application in Quantum Cosmology

et al. 2016

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We review the Eulerian description of hydrodynamics using Seliger-Whitham's formalism (in classical case) and Schutz's formalism (in relativistic case). In these formalisms, the velocity field of a perfect fluid is described by scalar potentials.With this we can obtain the evolution equations of the fluid and its Hamiltonian.In the scenario of quantum cosmology the Schutz's formalism makes it possible to introduce phenomenologically a time variable in minisuperspace models.PACS number(s): 98.80.Cq, 98.80.Qc

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“…On the other hand, an exact solution of field equations for Kantowski-Sachs background space with cosmological constant was found in [43]. For some other we refer the reader to [21,[44][45][46][47][48][49][50][51][52][53][54][55] and references therein. In the case of Einstein-Aether theory in [56] the authors presented a generic static spherical symmetric solution, where it has been shown that the Schwarzschild spacetime is recovered.…”

Section: Introductionmentioning

confidence: 99%

Exact Kantowski–Sachs spacetimes in Einstein–Aether scalar field theory

2020

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Exact and analytic solutions in Einstein–Aether scalar field theory with Kantowski–Sachs background space are determined. The theory of point symmetries is applied to determine the functional form of the unknown functions which defines the gravitational model. Conservation laws are applied to reduce the order of the field equations and write the analytic solution. Moreover, in order to understand the physical behaviour of the cosmological model a detailed analysis of the asymptotic behaviour for solutions of the gravitational field equations is performed.

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The Kantowski-Sachs Quantum Model with Stiff Matter Fluid

Cited by 4 publications

References 39 publications

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

Dynamics of a Perfect Fluid Through Velocity Potentials with Application in Quantum Cosmology

Exact Kantowski–Sachs spacetimes in Einstein–Aether scalar field theory

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