Bianchi Spacetime Models of Types VI-VIII  

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)-a1007-wd [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].
@ Related topics: Saha G&C(10) [interacting spinor and scalar fields, with a cosmological constant]; Kao & Lin PRD(11) [anisotropically inflating, stability]; Saha a1507 [non-linear spinor fields].

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]; Manojlović & Miković ATMP(00)gq/99 [Painlevé III equation]; Nilsson et al CQG(00)gq/99 [non-tilted 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]; Sloan a1601 [anisotropic matter].
@ 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: Characterized by nij = (–1,+1,+1), vi = 0.
@ General references: 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]; Apostolopoulos & Tsamparlis GRG(03)gq [self-similar]; Shabbir et al G&C(10) [proper curvature collineations]; Starkov PLA(11) [compact invariant sets; no periodic, homoclinic, or heteroclinic orbits in the zero-level set of the Hamiltonian].
@ With matter: Banerjee et al ASS(90) [viscous fluid]; Horwood et al CQG(03)gq/02 [fluid, late-time]; Hervik & Lim CQG(06)gq/05 [tilted pfluid, late-time]; Saha G&C(13)-a1107 [restrictions on the components of the energy-momentum tensor]; Heißel GRG(12)-a1203 [with anisotropic matter].

main pageabbreviationsjournalscommentsother sitesacknowledgements
send feedback and suggestions to bombelli at – modified 9 apr 2016