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An elastic Lagrangian for An elastic Lagrangian for space-timespace-time

Angelo Tartaglia and Ninfa Radicella Angelo Tartaglia and Ninfa Radicella Dipartimento di Fisica, Politecnico Dipartimento di Fisica, Politecnico

di Torino and INFNdi Torino and INFN

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The universe: a dualistic The universe: a dualistic descriptiondescription

Space-time/Matter-energy

TG What is this?

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““Elastic” continuaElastic” continua

u

xμ

Xa

ξ

r

r’

'u

0X,...,X,Xf nN21

0X,...,X,Xh nN21

N+nN

N

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The strain is described by the differential change of u

b

a

b

a

Xu

Xu

NnNa

,....,1,....,1

b

a

b

a

Xx

xu

Xu

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MetricityMetricity

ddddXXdXdXdl

ba

abba

ab

2

dxdxdxdxg

dxdxxx

XXdXdXdlba

abba

ab

2

'''''2

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DefectsDefects

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The “elastic” approachThe “elastic” approach

C

Elastic modulus tensor

Stress tensor

Hooke’s law

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Isotropic mediumIsotropic medium

C

Lamé coefficients

2

Lorentz signature notation

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Correspondence with the usual way Correspondence with the usual way of thinkingof thinking

xdg221RS 4

matter2 L

“Kinetic” term Potential term

Geometry

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Fitting the data (307 SnIa)Fitting the data (307 SnIa)

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ΛCDM 2 = 1.019

CD 2 = 1.017

Reduced Reduced 22 of the fits of the fits (2 parameters)(2 parameters)

B =λ+2μ/3=(32) 10-7 Mpc-2 =(32) 10-52 m-2

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ConclusionConclusion

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

CD introduces the idea of a global CD introduces the idea of a global symmetry fixing defect.symmetry fixing defect.

Local effects coincide with GR effectsLocal effects coincide with GR effectsThe nature of space-time shows up only The nature of space-time shows up only

at the cosmic scale, where CD performs at the cosmic scale, where CD performs at least as well as other theories, at least as well as other theories, however providing a compact and however providing a compact and consistent pictureconsistent picture

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Space time and the etherSpace 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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A. Tartaglia, M. Capone, Int. Jour. Mod. Phys. D, 17, 275-299 (2008)

A. Tartaglia, N. Radicella, Phys. Rev. D, 76, 083501 (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. 248-264, 2009

A. Tartaglia, N. Radicella, arXiv:0903.4096