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**An elastic Lagrangian for space-time**

Angelo Tartaglia and Ninfa Radicella Dipartimento di Fisica, Politecnico di Torino and INFN Paris July MG12

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**The universe: a dualistic description**

Space-time/Matter-energy What is this? Paris July MG12

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“Elastic” continua Xa N+n N ξ r r’ xμ N Paris July MG12

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**The strain is described by the differential change of u**

Paris July MG12

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Metricity Paris July MG12

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Defects Paris July MG12

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**The “elastic” approach**

Stress tensor Hooke’s law Elastic modulus tensor Paris July MG12

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**Isotropic medium Lamé coefficients Lorentz signature notation**

Paris July MG12

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**Correspondence with the usual way of thinking**

Potential term “Kinetic” term Geometry Paris July MG12

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**Fitting the data (307 SnIa)**

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**Reduced 2 of the fits (2 parameters)**

2 = 1.017 CD 2 = 1.019 ΛCDM B =λ+2μ/3=(32) 10-7 Mpc =(32) m-2 Paris July MG12

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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 Paris July MG12 12

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**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 Paris July MG12

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**A. Tartaglia, N. Radicella, Phys. Rev. D, 76, 083501 (2007)**

A. Tartaglia, M. Capone, Int. Jour. Mod. Phys. D, 17, (2008) 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: Paris July MG12 14

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