Kantowski–Sachs cosmology with Vlasov matter

Fajman, David; Heißel, G.

doi:10.1088/1361-6382/ab2425

Cited by 11 publications

(19 citation statements)

References 42 publications

(181 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…3QΣ) > 0 is not invariant for the full system (93) and for the averaged equations ( 99)- (103). Hence, although D(t) remains close to zero for t < t * , where t * satisfies Ḋ(t * ) = 0, once the orbit crosses the initial region, D changes its monotony and it will strictly increase without bound for t > t * .…”

Section: The Fractional Energy Density Of Mattermentioning

confidence: 97%

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

et al. 2021

View full text Add to dashboard Cite

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.

show abstract

Section: The Fractional Energy Density Of Mattermentioning

confidence: 97%

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

et al. 2021

View full text Add to dashboard Cite

show abstract

“…Therefore, it is possible to obtain information about large-time behaviour of more complicated full system via an analysis of simpler averaged system equations. With this in mind, in [153] the long-term behavior of solutions of a general class of systems in standard form [2] (x, t) 0 , (…”

Section: General Class Of Systems With a Time-dependent Perturbation Parametermentioning

confidence: 99%

“…was studied; where H > 0 is strictly decreasing in t and lim t→∞ H (t) = 0. The following Theorem by [153] gives local-in-time asymptotics for system (37). Let the norm • denotes the standard discrete 1 -norm u :…”

Section: General Class Of Systems With a Time-dependent Perturbation Parametermentioning

confidence: 99%

“…Theorem 1 (Theorem 3.1 of [153]) Suppose H (t) > 0 is strictly decreasing in t and lim t→∞ H (t) = 0. Fix any > 0 with < H (0) and define t * > 0 such that = H (t * ).…”

Section: General Class Of Systems With a Time-dependent Perturbation Parametermentioning

confidence: 99%

“…Averaging theory was used in reference [151] to study periodic orbits of Hamiltonian systems describing a universe filled with a scalar field; and in reference [152] to study future asymptotics of LRS Bianchi type III cosmologies with a massive scalar field. In reference [153] a theorem about large-time behaviour of solutions of Spatially Homogeneous (SH) cosmology with oscillatory behaviour (when H is non negative and monotonic decreasing to zero) was 0123456789(). : V,-vol presented.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

et al. 2021

View full text Add to dashboard Cite

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.

show abstract

On the future of solutions to the massless Einstein–Vlasov system in a Bianchi I cosmology

Lee¹,

Nungesser²,

Paul³

2020

Gen Relativ Gravit

View full text Add to dashboard Cite

Kantowski–Sachs cosmology with Vlasov matter

Cited by 11 publications

References 42 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

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

On the future of solutions to the massless Einstein–Vlasov system in a Bianchi I cosmology

Contact Info

Product

Resources

About