Bianchi Type I Models  

In General > s.a. gravitational thermodynamics.
$ Def: Defined by the structure constants CABC = 0 of the additive group R3; Generalized Kasner solution.
* Vacuum: Solution given by ds2 = –dt2 + t2p_1 dx2 + t2p_2 dy2 + t2p_3 dz2, with i pi = i pi2 = 1; Can be parametrized by

p1 = –u (1+u+u2)–1 ,      p2 = (1+u) (1+u+u2)–1 ,      p3 = u (1+u) (1+u+u2)–1 .

Kasner Solution
* Idea: Cosmological solution to Einstein's equation for the Bianchi I case, in which some dimensions expand and some others contract in time (in 3+1 dimensions, one expands and two contract).
* With fluid: In general relativity with viscous fluid, it is not possible to obtain a model which satisfies the second law of thermodynamics and the dominant energy condition; This can be done in other theories, such as scalar-tensor gravity.
@ General references: Kasner TAMS(24); Chodos & Detweiler PRD(80) [from Kaluza-Klein]; Harvey GRG(90).
@ Generalized: Belinskii & Khalatnikov JETP(70) [mixmaster-like]; Krori & Barua PLA(87) [9+1-dimensional]; Gentle & Miller CQG(98)gq/97 [in Regge calculus]; Maceda et al EPJC(04)ht/03 [non-commutative].

Related Phenomena > s.a. bel-robinson; Boltzmann Equation; observables; gravitational radiation; Silent Universe.
@ Isotropization: Fay CQG(01)gq/03 [scalar-tensor + massive scalar], CQG(02)gq/03 [scalar-tensor + scalar + fluid]; Bronnikov et al G&C(02) [with spinor, vector and scalar fields]; Fliche et al IJMPD(03); Fay & Luminet CQG(04)gq/03 [+ scalar]; Fay GRG(05)gq [+ non-minimal scalar].
@ Perturbations: Banach JMP(99), JMP(99); Song NCB(00) [null geodesics]; Tsagas & Maartens CQG(00) [magnetized]; Pereira et al a0707.

With Various Types of Matter > s.a. dilaton.
@ + scalar: Frolov et al CQG(91) [massless, non-linear]; Folomeev & Gurovich GRG(00); Joy & Kuriakose PRD(00) [6, phase transition].
@ + fluid: Huang JMP(90)gq/03 [stiff fluid, shear viscosity]; Chimento PRD(03)gq [internal symmetry]; Belinchón ASS(05)gq/04, ASS(06)gq/04 [variable constants]; Saha IJTP(06)gq/05 [pfluid + quintessence]; Christodoulakis et al JMP(06)gq/05 [+ scalar, decoupling]; Sandin & Uggla a0806 [two tilted fluids].
@ + fluid, viscous: Brevik & Pettersen PRD(00)gq [no anisotropy]; Pradhan et al gq/05/FizB; Saha gq/07 [+ non-linear spinor].
@ + fluid + cosmological constant: Khalatnikov & Kamenshchik PLB(03)gq [dust + cc, generalized Heckmann–Schücking]; Saha MPLA(05)gq/04, Saha & Rikhvitsky PhyD(06)gq/04 [viscous, + cosmological constant], JPA(07) [viscous, + spinor and cosmological constant]; Saha ChJP(05)gq/04 [pfluid + dark energy].
@ + fluid + variable cosmological constant: Pradhan & Pandey ASS(06)gq/04 [viscous fluid]; Vishwakarma GRG(05)-a0801 [+ variable G]; Singh & Tiwari IJMPD(07) [LRS, stiff fluid]; Belinchón a0707 [+ variable G], a0707 [+ variable G and c].
@ + spinor: Zhelnorovich JETP(04)gq/00 [Einstein-Dirac]; Saha PRD(01)gq, & Boyadjiev gq/03/IJMPA [+ cosmological constant], PRD(04)gq/03 [+ scalar]; Vakili & Sepangi JCAP(05)gq [m > 0, and signature change], AP(08)-a0709 [time reparameterization]; Saha PRD(06) [phenomenology].
@ Einstein-Vlasov: Rendall JMP(96)gq/95; Heinzle & Uggla CQG(06)gq/05.
@ Einstein-Maxwell: LeBlanc CQG(97) [magnetic, asymptotic states]; Balakin CQG(07)-a0710 [magnetized].
@ Einstein-Yang-Mills: Darian & Künzle CQG(96); Barrow et al PRD(05) [+ pfluid]; Narita CQG(06) [+dilaton].
@ Other matter: Harko & Mak IJMPD(02)gq [dilaton + magnetic field]; Villalba & Greiner MPLA(02)gq [particle creation]; Balakin & Zimdahl PRD(05)ap [non-minimal B field]; King & Coles CQG(07)ap/06 [B field + cosmological constant]; Calogero & Heinzle CQG(07)-a0706 [non-tilted elastic matter]; Folomeev IJMPD(07) [2 interacting scalar fields].

References > s.a. born-infeld; brans-dicke; Collineations; kaluza-klein; minisuperspace quantum cosmology; scalar-tensor.
@ General: Heckmann & Schücking in(62); Misner ApJ(68); Schön pr(91 [new variables]; Bachmann & Schmidt PRD(00)gq/99 [quantum cosmology bifurcation]; Hervik CQG(00)gq [moduli space & solutions]; Tsamparlis & Apostolopoulos JMP(00)gq [symmetries]; Khvedelidze & Mladenov PRD(02)gq [and 3-body Euler-Calogero-Sutherland model].
@ Scalar-tensor: Fay GRG(00)gq, GRG(00)gq, CQG(00)gq/03, CQG(00), CQG(00), CQG(01); Cataldo et al PRD(01)gq/00 [viscous]; Kumar & Singh IJTP(08) [Saez-Ballester theory].
@ Brane world: Toporensky CQG(01) [shear dynamics]; Harko & Mak CQG(03)gq/02 [viscous]; Toporensky & Tretyakov G&C(05)gq [recollapsing].
@ Other theories: Demaret et al CQG(99)gq/98 [type I, conformal gravity]; Chen et al PRD(00)ht/99 [N = 2, D = 5 supergravity]; Harko et al NCB(99) [Einstein-Cartan]; Pradhan & Vishwakarma JGP(04) [Lyra geometry]; Salti & Havare gq/05 [teleparallel, energy-momentum]; Leach et al CQG(06)gq [f(R) gravity]; > s.a. bianchi models.

Quantization > see minisuperspace; semiclassical general relativity.

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