Abstract
We present an elementary account of mathematical cosmology through a series of important unsolved problems. We introduce the fundamental notion of a cosmology and focus on the issue of singularities as a theme unifying many current, seemingly unrelated trends of this subject. We discuss problems associated with the definition and asymptotic structure of the notion of cosmological solution and also problems related to the qualification of approximations and to the ranges of validity of given cosmologies.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Hawking, S.W., and G.ER. Ellis, The large-scale structure of space-time, (CUP, 1973).
Wheeler, J.A. Superspace and the nature of quantum geometrodynamics, in C.M. DeWitt and I.A. Wheeler (eds.), (Benjamin, 1968); see also, C.W. Misner, Minisuperspace, in J. Klauder (ed.), Magic without magic, (Freeman, 1972).
Ellis, G.F.R., and H. van Elst, Cosmological Models, Cargèse lectures 1998, gr-qc/9812046.
Cotsakis, S., Introduction to Mathematical Cosmology, (in preparation, 2001).
Barrow, J.D., and F.J. Tipler, The Anthopic Cosmological Principle, (OUP, 1986).
Belinski, V.A., E.M. Lifshitzand I.M. Khalatnikov, Sov. Phys. Usp. 13, 745 (1971).
Belinski, V.A., I.M. Khalatnikov and E.M. Lifshitz, Adv. Phys. 13, 639 (1982).
Barrow, J.D. Phys. Rep. 85, 97 (1982).
Misner, C.W., in D. Hobill et al. (Eds.), Deterministic chaos in general relativity, (Plenum, 1994) pp. 317–328.
Barrow, J.D., and A. Ottewill, J. Phys. A. 16 2757 (1983).
Barrow, J.D., and D.H. Sonoda, Phys. Rep. 139, 1 (1986).
Cotsakis, S., and G.P. Flessas, Phys. Rev. D48, 3577 (1993).
Wainwright, I., and G.F.R. Ellis, Dynamical systems in cosmology, (CUP, 1997).
Hale, J., and H. Koçak, Dynamics and bifurcations, (Springer-Verlag, 1991).
Belinski, V.A., and I.M. Khalatnikov, Sov. Phys. JETP. 36, 591 (1972).
Berger, B.K. Phys. Rev. D61, 023508 (2000).
Bogoyavlenski, O.I., and S.P. Novikov, JETP. 64, 1475 (1973).
Bogoyavlenski, O.I. Dynamical systems in Astrophysics, (Springer-Verlag, 1986).
Barrow, J.D., and S. Cotsakis, Phys. Lett. B258, 299 (1991).
Demaret, J., M. Henneaux, and P. Spindel, Phys. Lett. B164, 27 (1986); see also, A. Hosoya, L.G. Jensen,and J.A. Stein-Shabes, Nucl. Phys. B283, 657 (1987).
Barrow, J.D., and M.P. Dabrowski, String cosmology and chaos, gr-qc/9806023.
Damour, T., and M. Henneaux, Phys. Rev. Lett. 85, 920 (2000); see also, T. Damourand M. Henneaux, Phys.Lett. B488, 108 (2000).
Barrow, J.D., and S. Cotsakis, Phys. Lett. B214, 515 (1988).
Faraoni, V., E. Gunzig and P. Nardone, Fund. Cosm. Phys. 20, 121 (1999).
Berger, B.K., et al., Mod. Phys. Lett. A13, 1565 (1998); see also,B. K. Berger, Approach to the Singularity in Spatially Inhomogeneous Cosmologies, gr-qc/Ol06009.
Ellis, G.F.R., et al, Phys. Rep. 124, 316 (1985).
Ellis, G.F.R., and W. Stoeger, Class. Quant. Grav. 4, 1697 (1987).
Christodoulou, D. Class. Quant. Grav. 16, A23 (1999).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Cotsakis, S. (2002). Current Trends in Mathematical Cosmology. In: Plionis, M., Cotsakis, S. (eds) Modern Theoretical and Observational Cosmology. Astrophysics and Space Science Library, vol 276. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0622-4_1
Download citation
DOI: https://doi.org/10.1007/978-94-010-0622-4_1
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-3931-4
Online ISBN: 978-94-010-0622-4
eBook Packages: Springer Book Archive