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Paris July MG121 An elastic Lagrangian for space-time Angelo Tartaglia and Ninfa Radicella Dipartimento di Fisica, Politecnico di Torino and INFN

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Paris July MG122 The universe: a dualistic description Space-time/Matter-energy What is this?

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Paris July MG123 Elastic continua xμxμ XaXa ξ r r N+n N N

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Paris July MG124 The strain is described by the differential change of u

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Paris July MG125 Metricity

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Paris July MG126 Defects

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Paris July MG127 The elastic approach Elastic modulus tensor Stress tensor Hookes law

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Paris July MG128 Isotropic medium Lamé coefficients Lorentz signature notation

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Paris July MG129 Correspondence with the usual way of thinking Kinetic term Potential term Geometry

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Paris July MG Fitting the data (307 SnIa)

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Paris July MG1211 ΛCDM 2 = CD 2 = Reduced 2 of the fits (2 parameters) B =λ+2μ/3=(3 2) Mpc -2 =(3 2) m -2

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Paris July MG Conclusion The CD theory is a theory of space-time preserving all general features of GR. CD introduces the idea of a global symmetry fixing defect. Local effects coincide with GR effects The nature of space-time shows up only at the cosmic scale, where CD performs at least as well as other theories, however providing a compact and consistent picture

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Paris July MG1213 Space time and the ether …. according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether. ……. But this ether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. …… Albert Einstein, Leiden, 1920

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Paris July MG A. Tartaglia, M. Capone, Int. Jour. Mod. Phys. D, 17, (2008) A. Tartaglia, N. Radicella, Phys. Rev. D, 76, (2007) A. Tartaglia, M. Capone, V. Cardone, N. Radicella, Int. Jour. Mod. Phys. D, 18, n. 3, 1-12 (2009) A. Tartaglia, Geometry, Integrability and Quantization X., Varna, Bulgaria, 6-11 June 2008, Publisher SOFIA: Avangard Prima, p , 2009 A. Tartaglia, N. Radicella, arXiv:

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