Types
of Bianchi Models| Types
of Bianchi Models |
Type I > see bianchi I.
Type II > s.a. bianchi models [higher-order
theories]; cosmological
perturbations; minisuperspace quantum
cosmology.
$ Def: Characterized
by nAB =
diag(1,0,0), and
vA = 0.
@ + fluid: Banerjee et al ASS(90)
[viscous]; Nilsson & Uggla JMP(97)gq;
Hewitt et al GRG(01)gq/00 [tilted].
@ + fluid + Maxwell: LeBlanc CQG(98)
[magnetic, asymptotic states].
@ Related topics: & Taub; Christodoulakis et al JMP(01)
[most general vacuum]; van den Hoogen & Ibáñez
PRD(03)gq/02 [branes];
Aydogdu IJMPD(06)gq/05,
IJMPA(06)gq [energy-momentum
density]; Belinchón ASS(09)-a0901 [with
time-varying constants, self-similar approach]; Valent GRG(09)
[Einstein metrics].
Type III
@ References: Chakraborty & Chakraborty IJMPD(02)
[Brans-Dicke, inflation]; Tanimoto et al CQG(03)gq/02,
CM(03)gq [spatially
closed, perturbations]; Christodoulakis & Terzis JMP(06)gq/04,
CQG(07)gq/06 [general
vacuum solution]; Shabbir gq/06 [Weyl
collineations]; Coley & Hervik CQG(08)-a0802 [tilted
pfluid]; Valent a0806,
GRG(09) [Einstein metrics, and geodesic flow]; Belinchón CQG(09)
[self-similar approach].
Type IV
@ References: Hervik et al CQG(05)gq/04 [tilted
pfluid, asymptotic behavior].
Type V > s.a. brans-dicke
theory; inflation; kaluza-klein
theory;
minisuperspace quantum cosmology.
@ General references: Joseph PCPS 62(66)87–89,
Hojman et al PRD(92)
[Hamiltonian from equations of motion]; Christodoulakis et al JMP(01)
[most general]; Bona & Palou
JMP(89) [3+1];
Coley & van den Hoogen JMP(94);
Valent a0806,
GRG(09) [Einstein metrics]; Kashif et al a0810-in
[symmetries of the Weyl tensor].
@ + fluid: Ram IJTP(90)
[perfect fluid]; Goliath & Nilsson JMP(00)gq [2-fluid,
irrotational]; Krasinski JMP(01)gq/00 [rotating,
dust]; Pradhan & Rai
ASS(04)gq/03 [tilted
viscous fluid]; Singh NCB(04)
[viscous]; Pradhan & Srivastav RRP(07)gq/04 [tilted viscous, varying cosmological constant], CzJP(05)gq/04
[pfluid, varying cosmological constant];
Christodoulakis et al JMP(06)gq [+
scalar, decoupling]; Bradley & Eriksson PRD(06)gq/05 [tilted,
numerical]; Pradhan et al gq/06 [with
bulk viscosity], a0704 [viscous,
with variable cosmological constant].
@ Other matter: Singh & Chaubey IJMPD(06)
[Einstein-Maxwell-dilaton]; Singh IJMPA(08)
[massive scalar, in Lyra geometry]; Reddy IJTP(09) [massless scalar, inflationary
model].
@ Related topics: Harvey NCB(97) [anisotropic];
Harko et al NCB(99) [Einstein-Cartan]; Banach JMP(99), JMP(99)
[perturbations]; Christodoulakis et al
PLA(00)gq/99 [diffuse
matter];
Camci & Türkyilmaz GRG(04)
[Ricci collineations]; Camci IJMPD(05)
[matter
collineations]; Camci et al JGP(09)
[curvature and Weyl collineations]; Sharif & Shamir CQG(09)-a0910 [vacuum f(R)
gravity, and I].
Type VI > s.a. gravitational
instanton and thermodynamics; inflation;
minisuperspace quantum cosmology; singularities.
* Types: VI0 and
VIh, including the exceptional case
VI–1/9.
@ VI0: Rosquist & Jantzen PLA(85);
LeBlanc et al CQG(95)
[magnetic, asymptotic states]; Berger CQG(96)gq/95 [chaotic
singularity]; Weaver CQG(00)gq/99 [magnetic,
and singularity]; Chakraborty & Ghosh
IJMPD(03)
[Brans-Dicke, inflation]; Barrow & Hervik CQG(03)gq,
Apostolopoulos GRG(04)gq/03,
Hervik CQG(04)gq [tilted
fluid]; Coley & Hervik CQG(04)gq [tilted
pfluids]; Singh & Chaubey IJMPD(06)
[Einstein-Maxwell-dilaton]; Heinzle & Ringström CQG(09)
[vacuum, future asymptotics]; Belinchón CQG(09)
[self-similar approach].
@ VI–1/9: Hewitt GRG(91);
Hewitt et al CQG(03)gq;
Hervik et al CQG(08)-a0706 [tilted
pfluid, late-time behavior].
@ VIh: & Ellis & MacCallum;
Clancy
et al PLB(99)gq [string
cosmology]; Jones gq/99 [semiclassical
cosmology]; Coley & Hervik CQG(05)gq/04 [pfluid];
Apostolopoulos GRG(05),
Hervik et al CQG(07)gq [tilted
pfluid].
Type VII > s.a. brans-dicke
theory; gravitational
instanton; minisuperspace quantum
cosmology; singularities.
* Types: VII0 and
VIIh; & Lukash.
* Behavior: VIIh models are asymptotically self-similar at late
times, VII0 show self-similarity breaking.
@ VII0: Wainwright et al CQG(99)gq/98 [pfluid];
Manojlovic & Mikovic
ATMP(00)gq/99 [Painlevé III
equation]; Nilsson et al CQG(00)gq/99 [nontilted
pfluid]; Horwood & Wainwright GRG(04)gq/03 [electrovac];
Hervik et al CQG(06)gq/05 [tilted
pfluid, asymptotic future]; Lim et al CQG(06)gq
[irrotational radiation].
@ VIIh: van
den Hoogen et al PRD(97)
[isotropization]; Wainwright et al CQG(98)
[isotropization]; Nayak G&C(02)
[imperfect fluid]; Coley & Hervik CQG(05)gq/04,
Hervik et al CQG(05)gq/04
[pfluid]; Barrow & Tsagas CQG(05)gq/04 [Lukash
plane wave metric]; Jaffe et al ApJ(06)ap/05
[with dark energy], A&A(06)ap
[and WMAP 3-year data]; Terzis & Christodoulakis GRG(09) [vacuum, general solution]; > s.a. cmb
anisotropy.
Type VIII > s.a. chaos in bianchi models.
$ Def: nAB =
(–1,+1,+1), vA =
0.
@ Dynamics: Banerjee et al ASS(90)
[viscous fluid]; Kirillov & Montani PRD(97)
[statistical properties, and IX];
Ringström
CQG(00)gq/99 [curvature
near singularity, and IX]; Barrow & Gaspar
CQG(01)gq,
Ringström CQG(01)gq, CQG(03)gq [vacuum,
late-time]; Horwood et al CQG(03)gq/02 [fluid,
late-time]; Apostolopoulos & Tsamparlis
GRG(03)gq [self-similar];
Hervik & Lim CQG(06)gq/05 [tilted
pfluid, late-time].
Type IX > see bianchi IX models; chaos in bianchi models.
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nov
2009