An elastic Lagrangian for spacetime Angelo Tartaglia and

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An elastic Lagrangian for space-time Angelo Tartaglia and Ninfa Radicella Dipartimento di Fisica, Politecnico

An elastic Lagrangian for space-time Angelo Tartaglia and Ninfa Radicella Dipartimento di Fisica, Politecnico di Torino and INFN Paris July 16 2009 MG 12 1

The universe: a dualistic description Space-time/Matter-energy What is this? Paris July 16 2009 MG

The universe: a dualistic description Space-time/Matter-energy What is this? Paris July 16 2009 MG 12 2

“Elastic” continua N+n N ξ r xμ Xa Paris July 16 2009 r’ MG

“Elastic” continua N+n N ξ r xμ Xa Paris July 16 2009 r’ MG 12 N 3

The strain is described by the differential change of u Paris July 16 2009

The strain is described by the differential change of u Paris July 16 2009 MG 12 4

Metricity Paris July 16 2009 MG 12 5

Metricity Paris July 16 2009 MG 12 5

Defects Paris July 16 2009 MG 12 6

Defects Paris July 16 2009 MG 12 6

The “elastic” approach Stress tensor Hooke’s law Elastic modulus tensor Paris July 16 2009

The “elastic” approach Stress tensor Hooke’s law Elastic modulus tensor Paris July 16 2009 MG 12 7

Isotropic medium Lamé coefficients Lorentz signature notation Paris July 16 2009 MG 12 8

Isotropic medium Lamé coefficients Lorentz signature notation Paris July 16 2009 MG 12 8

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

Correspondence with the usual way of thinking Potential term “Kinetic” term Geometry Paris July 16 2009 MG 12 9

Fitting the data (307 Sn. Ia) Paris July 16 2009 MG 12 10 10

Fitting the data (307 Sn. Ia) Paris July 16 2009 MG 12 10 10

2 Reduced of the fits (2 parameters) CD 2 = 1. 017 ΛCDM 2

2 Reduced of the fits (2 parameters) CD 2 = 1. 017 ΛCDM 2 = 1. 019 B =λ+2μ/3=(3 2) 10 -7 Mpc-2 =(3 2) 10 -52 m-2 Paris July 16 2009 MG 12 11

Conclusion The CD theory is a theory of space-time preserving all general features of

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 16 2009 MG 12 12 12

Space time and the ether …. according to the general theory of relativity space

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 16 2009 MG 12 13

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

A. Tartaglia, N. Radicella, Phys. Rev. D, 76, 083501 (2007) A. Tartaglia, M. Capone, Int. Jour. Mod. Phys. D, 17, 275299 (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. 248 -264, 2009 A. Tartaglia, N. Radicella, ar. Xiv: 0903. 4096 Paris July 16 2009 MG 12 14 14

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