Spatially Homogeneous Cosmological Models (Bianchi Models)

1. Kasner E: Geometrical Theorems on Einstein's Cosmological Equations, Amer. J. Maths. 43 (1921), 217
2. Kantowski R and R K Sachs: Some Spatially Homogeneous Anisotropic Relativistic Cosmological Models, J. Math. Phys. 7 (1966), 443
3. Misner C W: The Isotropy of the Universe, Astrophys. J. 151 (1968), 431
   NB: Type-I.
4. Ellis G F R, M A H MacCallum: A Class of Homogeneous Cosmological Models, Commun. Math. Phys. 12 (1969), 108
5. Misner C W: Mixmaster Universe, Phys. Rev. Lett. 22 (1969), 1071
6. MacCallum M A H, J M Stewart, B G Schmidt: Anisotropic Stresses in Homogeneous Cosmologies, Commun. Math. Phys. 17 (1970), 343
7. Collins C B: More Qualitative Cosmology, Commun. Math. Phys. 23 (1971), 137
   NB: Type-I/II/III/V/VI$_{h}$.
8. Collins C B, J M Stewart: Qualitative Cosmology, Mon. Not. R. Astron. Soc. 153 (1971), 419
9. Collins C B, S W Hawking: Why is the Universe Isotropic?, Astrophys. J. 180 (1973), 317
   NB: Focuses on Type-VII$_{h}$ and Type-VII$_{0}$ as they respectively contain the $k = -\,1$ and $k = 0$ FLRW cases. "Since it would seem that the existence of galaxies is a necessary condition for the development of intelligent life, the answer to the question `why is the Universe isotropic?' is `because we are there!'". Minimizes the chances that Misner's model might be realistic.
10. Collins C B and S W Hawking: The Rotation and Distortion of the Universe, Mon. Not. R. Astron. Soc. 162 (1973), 307
11. King A R, G F R Ellis: Tilted Homogeneous Cosmological Models, Commun. Math. Phys. 31 (1973), 209
12. MacCallum M A H: Cosmological Models from a Geometric Point of View, in Cargèse Lectures in Physics Vol. 6, Ed. E Schatzman, (New York: Gordon and Breach, 1973), 61
13. Jantzen R T: The Dynamical Degrees of Freedom in Spatially Homogeneous Cosmology, Commun. Math. Phys. 64 (1979), 211
14. Bradley J M, E Sviestins: Some Rotating, Time Dependent Bianchi Type VIII Cosmologies with Heat Flow, Gen. Rel. Grav. 16 (1984), 1119
15. Hsu L, J Wainwright: Self-Similar Spatially Homogeneous Cosmologies: Orthogonal Perfect Fluid and Vacuum Solutions, Class. Quantum Grav. 3 (1986), 1105
16. Jantzen R T: Spatially Homogeneous Dynamics: A Unified Picture, Gamov Cosmology, Proceedings of the LXXXVI Enrico Fermi Summer School, Ed. R Ruffini, F Melchiorri, (Amsterdam: North Holland, 1987)
17. Wainwright J, L Hsu: A Dynamical Systems Approach to Bianchi Cosmologies: Orthogonal Models of Class A, Class. Quantum Grav. 6 (1989), 1409
18. Burd A B, et al: A Numerical Analysis of Chaotic Behaviour in Bianchi IX Models, Gen. Rel. Grav. 22 (1990), 349
19. Lin X-F, R M Wald: Proof of the Closed-Universe Recollapse Conjecture for General Bianchi Type-IX Cosmologies, Phys. Rev. D 41 (1990), 2444
    NB: Lin X-F, R M Wald, Phys. Rev. D 40 (1989), 3280.
20. Uggla C: New Exact Perfect Fluid Solutions of Einstein's Equations, Class. Quantum Grav. 7 (1990), L171
    NB: Type-VI$_{h}$, $p=0\ / \ \sfrac{1}{5}\,\mu$.
21. Uggla C, K Rosquist: New Exact Perfect Fluid Solutions Of Einstein's Equations: II, Class. Quantum Grav. 7 (1990), L279
    NB: Type-VI$_{h}$.
22. Uggla C, K Rosquist, R T Jantzen: Geometrizing the Dynamics of Bianchi Cosmology, Phys. Rev. D 42 (1990), 404
23. Uggla C, H von Zur-Mühlen: Compactified and Reduced Dynamics for Locally Rotationally Symmetric Bianchi Type IX Perfect Fluid Models, Class. Quantum Grav. 7 (1990), 1365
24. Burd A B, N Buric, R K Tavakol: Chaos, Entropy and Cosmology, Class. Quantum Grav. 8 (1991), 123
    NB: Type-IX as an example.
25. Hewitt C G: An Exact Tilted Bianchi II Cosmology, Class. Quantum Grav. 8 (1991), L109
26. King D H: Gravity-Wave Insights to Bianchi Type-IX Universes, Phys. Rev. D 44 (1991), 2356
27. Coley A A, J Wainwright: Qualitative Analysis of Two-Fluid Bianchi Cosmologies, Class. Quantum Grav. 9 (1992), 651
    NB: Non-interacting fluids, LRS $G_{3}$II, 3-D phase portraits, different $\gamma$'s.
28. Fi\~{s}er K, K Rosquist, C Uggla: Bianchi Type V Perfect Fluid Cosmologies, Gen. Rel. Grav. 24 (1992), 679
    Excellent!!!
29. Hewitt C G, J Wainwright: Dynamical Systems Approach to Tilted Bianchi Cosmologies: Irrotational Models of Type V, Phys. Rev. D 46 (1992), 4242
    NB: LRS $G_{3}$V.
30. Jantzen R T, C Uggla: Structure of the Generalized Friedmann Problem, Gen. Rel. Grav. 24 (1992), 59
31. Maartens R, M F Wolvaardt: Some Exact Bianchi Solutions, Class. Quantum Grav. 9 (1992), 1525
    NB: Irrotational tilted Type-V (non-LRS) models with $\gamma=2$ perfect fluid.
32. Roy S R, S K Banerjee: Bianchi VI Cosmological Models Representing Perfect Fluid and Radiation with Electric-Type Free Gravitational Fields, Gen. Rel. Grav. 24 (1992), 1117
33. Sklavenites D: Geodesic Bianchi Type Cosmological Models, Gen. Rel. Grav. 24 (1992), 47
    NB: Perfect fluid, 2 commuting hypersurface orthogonal spacelike Killing Vector Fields, $\dot{u}^{\mu}=0$.
34. Coussaert O, M Henneaux: Bianchi Cosmological Models and Gauge Symmetries, Class. Quantum Grav. 10 (1993), 1607
35. Hewitt C G, J Wainwright: A Dynamical Systems Approach to Bianchi Cosmologies: Orthogonal Models of Class B, Class. Quantum Grav. 10 (1993), 99
36. Obregón O, J Pullin, M P Ryan: Bianchi Cosmologies: New Variables and a Hidden Supersymmetry, Phys. Rev. D 48 (1993), 5642
37. LeBlanc V G, D Kerr, J Wainwright: Asymptotic States of Magnetic Bianchi VI$_{0}$ Cosmologies, Class. Quantum Grav. 12 (1995), 513
    NB: OSH Type-VI$_{0}$, $\gamma$-law perfect fluid plus sourcefree magnetic Maxwell field matter source.
38. Schirmer J: Hamiltonian Reduction of Bianchi Cosmologies, Class. Quantum Grav. 12 (1995), 1099
    NB: Quite technical; deals with aspects of the automorphism group.
39. Uggla C, R T Jantzen, K Rosquist: Exact Hypersurface-Homogeneous Solutions in Cosmology and Astrophysics, Phys. Rev. D 51 (1995), 5522. Also: Preprint gr-qc/9503061.
40. Berger B K, D Garfinkle, E Strasser: New Algorithm for Mixmaster Dynamics, Class. Quantum Grav. 14 (1997), L29
41. Cornish N J, J J Levin: The Mixmaster Universe is Chaotic, Phys. Rev. Lett. 78 (1997), 998. Also: Preprint gr-qc/9605029.
42. Wainwright J, G F R Ellis (Eds.): Dynamical Systems in Cosmology, (Cambridge: Cambridge University Press, 1997)
43. Wainwright J, A A Coley, G F R Ellis, M Hancock: On the Isotropy of the Universe: Do Bianchi VII${}_{h}$ Cosmologies Isotropize?, Class. Quantum Grav. 15 (1998), 331
44. Nilsson U S, C Uggla, J Wainwright, W C Lim: An Almost Isotropic Cosmic Microwave Temperature does not Imply an Almost Isotropic Universe, Astrophys. J. 521 (1999), L1. Also: Preprint astro-ph/9904252.
45. Wainwright J, M J Hancock, C Uggla: Asymptotic Self-Similarity Breaking at Late Times in Cosmology, Class. Quantum Grav. 16 (1999), 2577. Also: Preprint gr-qc/9812010.
46. Ringström H: Curvature Blow Up in Bianchi VIII and IX Spacetimes, Class. Quantum Grav. 17 (2000), 713. Also: Preprint gr-qc/9911115.
    NB: Vacuum case. Employs the dimensionless orthonormal frame formulation of Wainwright and Hsu (1989).
47. Hewitt C G, R Bridson, J Wainwright: The Asymptotic Regimes of Tilted Bianchi II Cosmologies, Preprint gr-qc/0008037.

Selected References
Last revision: Thu, 17-8-2000 (This page is under construction)