Analysis of an FRW cosmological model

Konstantinos Andriopoulos 1  and Peter Leach
  • 1 Department of Information and Communication Systems Engineering, University of the Aegean, Karlovassi, GR-83200, Samos, Greece
  • 2 School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X54001, Durban, 4000, Republic of South Africa


The Einstein field equations for the Friedmann universe reduce to a system of three first-order equations for the space-like components and a constraint from the temporal component. We analyse the system from the viewpoints of symmetry and singularity analyses. The solutions of particular relevance to Cosmology are highlighted.

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  • [1] L.D. Landau, E.M. Lifshitz, The Classical Theory of Fields (Pergamon Press, Oxford, 1987)

  • [2] A. Linde, Particle Physics and Inflationary Cosmology (Harwood Academic Publishers, Amsterdam, 1990)

  • [3] M.P. Ryan Jr, L.C. Shepley, Homogeneous Relativistic Cosmologies (Princeton University Press, Princeton, New Jersey, 1975)

  • [4] S. Cotsakis, J.D. Barrow, The dominant balance at cosmological singularities Proceedings of the Greek Relativity meeting NEB12 (2006)

  • [5] M.J. Ablowitz, A. Ramani, H. Segur, J. Mat. Phys. 21 715 (1980)

  • [6] A. Ramani, B. Grammaticos, T. Bountis, Phys. Rep. 180, 159 (1989)

  • [7] M.C. Nucci, J. Mat. Phys. 37, 1772 (1996)

  • [8] K. Andriopoulos, P.G.L. Leach, G.P. Flessas, J. Math. Anal. Appl. 262, 256 (2001)

  • [9] K. Andriopoulos, Complete symmetry groups and Lie remarkability, In: Symmetry and Perturbation Theory — SPT 2007 G. Gaeta, R. Vitolo, S. Walcher Eds. (World Scientific, Singapore, 2007) 237

  • [10] P.G.L. Leach, S. Cotsakis, J. Miritzis, Gravitation & Cosmology 7, 311 (2001)

  • [11] J. Miritzis, P.G.L. Leach, Gravitation & Cosmology 6, 282 (2000)


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