# Possible physical universes

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## Abstract

The purpose of this paper is to discuss the various types of physical universe which could exist according to modern mathematical physics. The paper begins with an introduction that approaches the question from the viewpoint of ontic structural realism. Section 2 takes the case of the 'multiverse' of spatially homogeneous universes, and analyses the famous Collins-Hawking argument, which purports to show that our own universe is a very special member of this collection. Section 3 considers the multiverse of all solutions to the Einstein field equations, and continues the discussion of whether the notions of special and typical can be defined within such a collection.

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## References

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Turner, M.S. (2001). A Sober Assessment of Cosmology at the New Millennium. Publ. Astron. Soc. Pac. 113 pp653–657

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Wallace, D. (2001). Worlds in the Everett Interpretation, Studies in the History and Philosophy of Modern Physics, 33, pp637–661.

Callender, C. (2004). Measures, Explanations and the Past: Should “Special” Initial Conditions Be Explained?, British Journal for the Philosophy of Science, 55(2), pp195–217.

Collins, C.B., Hawking, S.W. (1973). Why Is the Universe Isotropic? The Astrophysical Journal, 180, pp316–334.

Derdzinski, A. (1992). Geometry of the Standard Model of Elementary Particles, Texts and Monographs in Physics, Berlin–Heidelberg–New York: Springer Verlag.

Earman, J., and Mosterin, J. (1999). A Critical Look at Inflationary Cosmology, Philosophy of Science 66, pp1–49.

Earman, J. (2002). Laws, Symmetry, and Symmetry Breaking; Invariance, Conservation Principles, and Objectivity, Presidential Address PSA 2002.

Ellis, G.F.R. (1999). 83 Years of General Relativity and Cosmology, Classical and Quantum Gravity, 16, A37.

Ellis, G.F.R. (2002). Cosmology and Local Physics, Int. J. Mod. Phys. A17, pp2667–2672.

Enderton, H.B. (2001). A Mathematical Introduction to Logic, Second Edition, London: Academic Press.

Hunt, B.R., Sauer, T., Yorke, J.A. (1992). Prevalence: a Translation–Invariant “Almost Every” on Infinite–dimensional Spaces. Bull. Amer. Math. Soc. 27 pp217–238.

Heller, H. (1992). Theoretical Foundations of Cosmology, Singapore: World Scientific.

Hewitt, C.G., Siklos, S.T.C., Uggla, C., Wainwright, J. (1997). Exact Bianchi Cosmologies and State Space, in Dynamical Systems in Cosmology, eds. J. Wainwright and G.F.R. Ellis, pp186–211. Cambridge: Cambridge University Press.

Isenberg, J., Marsden, J.E. (1982). A Slice Theorem for the Space of Solutions of Einstein’s Equations, Physics Reports 89, No. 2, p179–222.

Jantzen, R.T. (1987). Spatially Homogeneous Dynamics: A Unified Picture, in Proc. Int. Sch. Phys. E. Fermi Course LXXXVI (1982) on Gamov Cosmology (R. Ruffini, F. Melchiorri, Eds.), pp61–147. Amsterdam: North Holland.

Jensen, L.G., and Stein–Schabes, J.A. (1987). Is Inflation Natural?, Physical Review D35, pp1146–1150.

Ladyman, J. (1998). What is Structural Realism? Studies in History and Philosophy of Science, 29, pp409–424.

Linde, A.D. (1983a). Chaotic Inflating Universe. Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki 38, pp149–151. [English translation: Journal of Experimental and Theoretical Physics Letters 38, pp176–179.]

Linde, A.D. (1983b). Chaotic Inflation. Physics Letters 129B, pp177–181.

MacCallum, M.A.H. (1979). Anisotropic and Inhomogeneous Relativistic Cosmologies, in General Relativity: An Einstein Centenary, eds. S. Hawking and W. Israel, pp533–580. Cambridge: Cambridge University Press.

Mosterin, J. (2004). Anthropic Explanations in Cosmology, in Proceedings of the 12th International Congress of Logic, Methodology and Philosophy of Science, Hajek, Vald´es and Westerstahl (eds.). Amsterdam: North–Holland Publishing.

Rucker, R. (1982). Infinity and the Mind. Boston: Birkhauser. Smolin, L. (1997). The Life of the Cosmos, London: Weidenfeld and Nicolson.

Sneed, J.D. (1971). The Logical Structure of Mathematical Physics, Dordrecht: Reidel.

Suppe, F. (1989). The Semantic Conception of Theories and Scientific Realism, Urbana, Illinois: University of Illinois Press.

Suppes, P. (1969). Studies in the Methodology and Foundation of Science: Selected Papers from 1951 to 1969, Dordrecht: Reidel.

Tegmark, M. (1998). Is ‘the Theory of Everything’ Merely the Ultimate Ensemble Theory?, Annals of Physics, 270, pp1–51. arXiv:gr–qc/9704009.

Turner, M.S. (2001). A Sober Assessment of Cosmology at the New Millennium. Publ. Astron. Soc. Pac. 113 pp653–657

Wald, R.M. (1983). Phys. Rev. D 28, 2118.

Wallace, D. (2001). Worlds in the Everett Interpretation, Studies in the History and Philosophy of Modern Physics, 33, pp637–661.