1. Has elasticity anything to do with cosmology? Angelo Tartaglia RELGRAV

2. February 17 2011 RELGRAV 2 “Elastic” continua xμxμ XaXa ξaξa r r’ N+n N N

3. 3 Geometry and elasticity In a strained medium each point is in one to one correspondence with points in the unstrained state u, r and r’ are (N+n)-vectors in the flat embedding space February 17 2011 RELGRAV

4. February 17 2011 RELGRAV 4 The strain is described by the differential change of u

5. February 17 2011 RELGRAV 5 Metricity

6. What about space-time? February 17 2011 6 RELGRAV Space-time/Matter-energy What is this?

7. 7 Is it a mathematical artifact to describe the gravitational field and the global properties of the universe? Is it something real endowed with physical properties? What is space-time? February 17 2011 RELGRAV

8. A four-dimensional manifold February 17 2011 RELGRAV 8 Minkowski (flat) space-time General (curved) space-time

9. February 17 2011 RELGRAV 9 Defects in continua Flat reference frame Curved natural frame

10. 10 What consequences from a defect? The defect fixes the global symmetry A spontaneous strain tensor ε μν (or displacement vector field u a ) appears All this must show up in the Lagrangian of the strained manifold (space-time) February 17 2011 RELGRAV

11. February 17 2011 RELGRAV 11 Strained space-time dr 0 dr unstrained strained  gg Strain tensor

12. 12 The “elastic” approach Elastic modulus tensor Stress tensor Hooke’s law February 17 2011 RELGRAV

13. 13 Isotropic medium Lamé coefficients February 17 2011 RELGRAV Elastic energy

14. February 17 2011 RELGRAV 14 The Lagrangian density “Kinetic” term Potential term Geometry

15. February 17 2011 RELGRAV 15 Robertson-Walker symmetry z r r l l   =f(r)

16. Has the universe a R-W symmetry? February 17 2011 RELGRAV 16

17. February 17 2011 RELGRAV 17 The Hubble parameter from the Einstein equations A. Tartaglia and N. Radicella, CQG, 27, 035001 (2010)

18. 18 The distance modulus of bright objects Observed magnitude Absolute magnitude Hubble parameter Distances in Mpc February 17 2011 RELGRAV

19. February 17 2011 RELGRAV 19 19 Fitting the data (307 SnIa)

20. February 17 2011 RELGRAV 20 Other cosmological tests Primordial nucleosynthesis (correct proportion between He, D and hydrogen) CMB acoustic horizon Structure formation after the recombination era.

21. Nucleosynthesis In the early stages the universe is radiation- dominated X Boost

22. Large Scale Stractures Particle horizon at the equality epoch (z=3150) Constraint from LSS: Ω m0 : matter density in units of h: Hubble constant in units of km/(s  Mpc)

23. Acoustic scale of the CMB The power spectrum of the CMB depends on the expansion rate of the universe z ls  1090 last scattering D A :  angular diameter distance r s :  sound horizon

24. February 17 2011 RELGRAV 24 Bayesian posterior probability

25. February 17 2011 RELGRAV 25 Optimal value of the parameters N. Radicella, M. Sereno, A. Tartaglia

26. February 17 2011 RELGRAV 26 Schwarzschild symmetry Natural frame Reference frame (Minkowski) Gauge function

27. February 17 2011 RELGRAV 27 The strain tensor

28. February 17 2011 RELGRAV 28 Three field equations

29. February 17 2011 RELGRAV 29 Weak strain

30. February 17 2011 RELGRAV 30 Approximate solutions ,  = functions of,  ~, 

31. February 17 2011 RELGRAV 31 Post-Keplerian circular orbits Looks like the effect of dark matter Light rays

32. February 17 2011 RELGRAV 32 Conclusion The strained space-time theory introduces a strain energy of vacuum depending on curvature The idea of a cosmic defect explains why the symmetry of the universe should be R- W (or anything else) The theory accounts for the accelerated expansion of the universe and is consistent with BBN, structure formation, acoustic scale of the CMB and SnIa’s luminosity