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 n^AB = diag(1,0,0), and v_A = 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].

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 a0802 [tilted pfluid].

Type IV
@ References: Hervik et al CQG(05)gq/04 [tilted pfluid, asymptotic behavior].

Type V > s.a. brans-dicke; inflation; kaluza-klein; 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).
@ + 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 et al gq/04/IJMPD [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].
@ 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].

Type VI > s.a. gravitational instanton and thermodynamics; inflation; minisuperspace quantum cosmology; singularities.
* Types: VI₀ and VI_h, 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].
@ VI_–1/9: Hewitt GRG(91); Hewitt et al CQG(03)gq; Hervik et al CQG(08)-a0706 [tilted pfluid, late-time behavior].
@ VI_h: & 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; gravitational instanton; minisuperspace quantum cosmology; singularities.
* Types: VII₀ and VII_h; & Lukash.
* Behavior: VII_h 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].
@ VII_h: 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], ap/06/A&A [and WMAP 3-year data]; > s.a. cmb anisotropy.

Type VIII > s.a. chaos in bianchi models.
$ Def: n^AB = (–1,+1,+1), v_A = 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; chaos in bianchi models.

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