COSMOLOGICAL MODELS FROM A DYNAMICAL SYSTEMS PERSPECTIVE

Journal of Hyperbolic Differential Equations

Volumn 2, Issue 2, 2005, Pages 437-469

  Wainwright, J ^a   Lim, W C ^a,b  

^a UNIVERSITY OF WATERLOO   (Canada)

^b DALHOUSIE UNIVERSITY   (Canada)

Author keywords

cosmology; Dynamical systems

Indexed keywords

EID: 33744785880     PISSN: 02198916     EISSN: 17936993     Source Type: Journal    
DOI: 10.1142/S0219891605000531     Document Type: Article

References (49)

1. L. Andersson, H. van Elst and C. Uggla, Gowdy phenomenology in scale-invariant variables, Class. Quantum Grav. 21 (2004) S29–S57.
2. L. Andersson, H. van Elst, W. C. Lim and C. Uggla, Asymptotic silence of generic cosmological singularities, Phys. Rev. Lett. 94 (2005) 051101.
3. J. M. Bardeen, Gauge invariant cosmological perturbations, Phys. Rev. D22 (1980) 1882–1905.
4. J. D. Barrow, Quiescent cosmology, Nature 272 (1978) 211–215.
5. B. K. Berger, Hunting local Mixmaster dynamics in spatially inhomogeneous cosmologies, Class. Quantum Grav. 21 (2004) S81–S96.
6. 2 isometry, Phys. Rev. D64 (2001) 084006.
7. B. K. Berger and V. Moncrief, Numerical investigation of cosmological singularities, Phys. Rev. D48 (1993) 4676–4687.
8. A. A. Coley, Dynamical Systems and Cosmology (Kluwer Academic Publishers, 2003).
9. A. A. Coley, He and Lim, Isotropic singularity in inhomogeneous brane cosmological models, Class. Quantum Grav. 21 (2004) 1311–1342.
10. A. A. Coley and S. Hervik, Bianchi cosmologies: a tale of two tilted fluids, Class. Quantum Grav. 21 (2004) 4193–4208.
11. A. A. Coley and R. J. van den Hoogen, The dynamics of multi-scalar field cosmological models and assisted inflation, Phys. Rev. D62 (2000) 023517.
12. C. B. Collins, More qualitative cosmology, Commun. Math. Phys. 23 (1971) 137–156.
13. D. Eardley, E. P. Liang and R. K. Sachs, Velocity-dominated singularities in irrotational dust cosmologies, J. Math. Phys. 13 (1972) 99–107.
14. G. F. R. Ellis, Dynamics of pressure-free matter in general relativity, J. Math. Phys. 8 (1967) 1171–1194.
15. G. F. R. Ellis, The space of cosmological space–times, JHDE 2(2) (2005) 331–379.
16. G. F. R. Ellis and M. Bruni, Covariant and gauge-invariant approach to cosmological density fluctuations, Phys. Rev. D40 (1989) 1804–1818.
17. G. F. R. Ellis, J. Hwang and M. Bruni, Covariant and gauge-independent perfect-fluid Robertson-Walker perturbations, Phys. Rev. D40 (1989) 1819–1826.
18. G. F. R. Ellis and R. Maartens, The Emergent Universe: inflationary cosmology with no singularity, Class. Quantum Grav. 21 (2004) 223–232.
19. G. F. R. Ellis and M. A. H. MacCallum, A class of homogeneous cosmological models, Commun. Math. Phys. 12 (1969) 108–141.
20. H. van Elst and C. Uggla, General relativistic 1+3 orthonormal frame approach, Class. Quantum Grav. 14 (1997) 2673–2695.
21. 2 cosmology, Class. Quantum Grav. 19 (2002) 51–82.
22. D. Garfinkle, Numerical simulations of generic singularities, Phys. Rev. Lett. 93 (2004) 161101.
23. D. Garfinkle and M. Weaver, High velocity spikes in Gowdy spacetimes, Phys. Rev. D67 (2003) 124009.
24. M. Goliath and G. F. R. Ellis, Homogeneous cosmologies with a cosmological constant, Phys. Rev. D60 (1999) 023502.
25. S. W. Goode and J. Wainwright, Isotropic singularities in cosmological models, Class. Quantum Grav. 2 (1985) 99–115.
26. J. M. Heinzle, N. Rohr and C. Uggla, Matter and dynamics in closed cosmologies, Phys. Rev. D71 (2005) 083506.
27. 0 universes, Class. Quantum Grav. 21 (2004) 2301–2317.
28. C. G. Hewitt, R. Bridson and J. Wainwright, The asymptotic regimes of tilted Bianchi II cosmologies, Gen. Rel. Grav. 33 (2001) 65–94.
29. D. Hobill, A. Burd and A. A. Coley (eds.), Deterministic Chaos in General Relativity (Plenum Press, 1994).
30. J. T. Horwood and J. Wainwright, Asymptotic regimes of magnetic Bianchi cosmologies, Gen. Rel. Grav. 36 (2004) 799–823.
31. I. M. Khalatnikov, A. Yu. Kamenshchik, M. Martellini and A. A. Starobinsky, Quasi-isotropic solution of the Einstein equations near a cosmological singularity for a two-fluid cosmological model, J. Cosmol. Astropart. Phys. 03 (2003) 001.
32. A. R. King and G. F. R. Ellis, Tilted homogeneous cosmological models, Commun. Math. Phys. 31 (1973) 209–242.
33. J. Kristian and R. K. Sachs, Observations in cosmology, Astrophys. J. 143 (1966) 379–399.
34. V. G. LeBlanc, Bianchi II magnetic cosmologies, Class. Quantum Grav. 15 (1998) 1607–1626.
35. E. M. Lifshitz and I. M. Khalatnikov, Investigations in relativistic cosmology, Adv. Phys. 12 (1963) 185–249.
36. W. C. Lim, The Dynamics of Inhomogeneous Cosmologies, PhD thesis, University of Waterloo (2004), preprint gr-qc/0410126.
37. W. C. Lim, H. van Elst, C. Uggla and J. Wainwright, Asymptotic isotropization in inhomogeneous cosmology, Phys. Rev. D69 (2004) 103507.
38. P. K.-H. Ma and J. Wainwright, A dynamical systems approach to the oscillatory singularity in Bianchi cosmologies, in Relativity Today, ed. Z. Perjés (Nova Science Publishers, 1992).
39. R. Maartens, G. F. R. Ellis and W. R. Stoeger, Limits on anisotropy and inhomogeneity from the cosmic background radiation, Phys. Rev. D51 (1995) 1525–1535.
40. R. Maartens, G. F. R. Ellis and W. R. Stoeger, Anisotropy and inhomogeneity of the universe from ∆T/T, Astron. Astrophys. 309 (1996) L7–L10.
41. R. Penrose, Singularities and time-asymmetry, in General Relativity: An Einstein Centenary Survey, eds. S. W. Hawking and W. Israel (Cambridge University Press, 1979).
42. A. D. Rendall, Asymptotics of solutions of the Einstein equations with positive cosmological constant, Annales Henri Poincaré 5 (2004) 1041–1064.
43. A. D. Rendall and M. Weaver, Manufacture of Gowdy spacetimes with spikes, Class. Quantum Grav. 18 (2001) 2959–2976.
44. H. Ringström, The Bianchi IX attractor, Annales Henri Poincaré 2 (2001) 405–500.
45. R. K. Sachs and A. M. Wolfe, Perturbation of a cosmological model and angular variations of the microwave background, Astrophys. J. 147 (1967) 73–90.
46. C. Uggla, H. van Elst, J. Wainwright and G. F. R. Ellis, Past attractor in inhomogeneous cosmology, Phys. Rev. D68 (2003) 103502.
47. J. Wainwright, M. J. Hancock and C. Uggla, Asymptotic self-similarity breaking at late times in cosmology, Class. Quantum Grav. 16 (1999) 2577–2598.
48. J. Wainwright and G. F. R. Ellis (eds.), Dynamical Systems in Cosmology (Cambridge University Press, 1997).
49. R. M. Wald, Asymptotic behaviour of homogeneous cosmological models in the presence of a positive cosmological constant, Phys. Rev. D28 (1983) 2118–2120.