1. TeVPA08 Beijing -24 September 2008 1 Space-time defects and the accelerated expansion of the universe: an alternative to dark energy? Angelo Tartaglia DIFIS – Politecnico and INFN Torino, Italy

2. TeVPA08 Beijing -24 September 2008 2 Plan of the talk Starting point and motivation Starting point and motivation Outline of the Cosmic Defect theory Outline of the Cosmic Defect theory Fit of the observational data Fit of the observational data Open problems Open problems

3. TeVPA08 Beijing -24 September 2008 33 Inflation Gravity in clusters and galaxies Accelerated expansion There is something missing Modify GR Introduce new fields in standard GR Give up GR and look for another theory Puzzles of standard cosmology

4. TeVPA08 Beijing -24 September 2008 44 Accept a four- (N-) dimentional spacetime manifold Add “matter” components Isotropy and homogeneity Perfect fluid

5. TeVPA08 Beijing -24 September 2008 55 Λ Cold Dark Matter Simplest and most effective model for the universe; however: “matter” must be 7 times more than what we “see” (~30% of the cosmic source); Λ corresponds to 70% of the cosmic souce but … what is Λ?

6. TeVPA08 Beijing -24 September 2008 66 The Cosmic Defect theory: strain in a continuum N-dimensional “sheet” Strain induced by boundary conditions Elasticity

7. TeVPA08 Beijing -24 September 2008 77 A defect Internal “spontaneous” strain state

8. TeVPA08 Beijing -24 September 2008 88 Geometry, elasticity and defects Reference manifold Natural manifold

9. TeVPA08 Beijing -24 September 2008 99 In a strained medium each point is in one to one correspondence with points in the unstrained state In the purely elastic case the new situation is diffeomorphic to the old one  may be expressed as a function of x as well as of ξ Intrinsic coordinatesExtrinsic coord. Displacement

10. TeVPA08 Beijing -24 September 2008 1010 Induced metric Strain tensor (represented in the reference manifold)

11. TeVPA08 Beijing -24 September 2008 1111 “Radial” displacement field (space isotropy and homogeneity) Strained

12. TeVPA08 Beijing -24 September 2008 1212 A Robertson-Walker universe

13. TeVPA08 Beijing -24 September 2008 1313 How can we choose a Lagrangian expressing the presence of the defect? Start from the phase space of a Robertson-Walker universe and look around for similar phase spaces

14. TeVPA08 Beijing -24 September 2008 1414 Phase space analogy FRW universe Inertial expansion Accelerated expansion Decelerated expansion Point particle Free motion Driving force Braking force

15. TeVPA08 Beijing -24 September 2008 1515 A simple classical problem Motion of a point massive particle in a viscous medium

16. TeVPA08 Beijing -24 September 2008 1616 Spacetime “Dissipative” action integral Same structure as in the classical simple case The “viscous” properties of space-time are contained in the vector field 

17. TeVPA08 Beijing -24 September 2008 1717 Impose the 4-isotropy around the origin and use cosmic time as the “radial” coordinate

18. TeVPA08 Beijing -24 September 2008 1818 Symmetry and application of the minimal action principle do not commute Defect means Symmetry first

19. TeVPA08 Beijing -24 September 2008 1919 Divergence free vector

20. TeVPA08 Beijing -24 September 2008 2020 Expansion rate Accelerated expansion Asymptotic stop

21. TeVPA08 Beijing -24 September 2008 2121 Expansion versus cosmic time Inflation Acceleration

22. TeVPA08 Beijing -24 September 2008 2222 Fitting the data from SnIa One has to account for the presence of matter

23. TeVPA08 Beijing -24 September 2008 2323 Distance modulus vs z (192 SnIa)

24. TeVPA08 Beijing -24 September 2008 2424 ΛCDM  2 = 1.029 CD  2 = 1.092 Reduced  2 of the fits

25. TeVPA08 Beijing -24 September 2008 2525 The Hubble parameter H 0 = (62.8 ± 1.7) km/s  Mpc Most models ~64 km/s  Mpc Observation~75 km/s  Mpc

26. TeVPA08 Beijing -24 September 2008 2626 Weaknesses and open problems Fitting the SnIa luminosity data with a logarithmic function and two parameters is “too easy” Fitting the SnIa luminosity data with a logarithmic function and two parameters is “too easy” The heuristic definition of the Lagrangian (though working) needs more stringent arguments: why is it working? The heuristic definition of the Lagrangian (though working) needs more stringent arguments: why is it working?

27. TeVPA08 Beijing -24 September 2008 2727 The null divergence condition should be a consequence of the singularity in correspondence of the defect, rather than a formal constraint imposed on the vector. The null divergence condition should be a consequence of the singularity in correspondence of the defect, rather than a formal constraint imposed on the vector.

28. TeVPA08 Beijing -24 September 2008 2828 Correspondences Defect theory in solids Defect theory in solids Bimetric theories: “pre-shaped container” Bimetric theories: “pre-shaped container” Vector-tensor theories Vector-tensor theories Curvature fluid Curvature fluid

29. TeVPA08 Beijing -24 September 2008 2929 Final remarks The CD theory provides a consistent physical interpretation of space-time giving a heuristic tool to move across the Lagrangian “forest” set up by Lagrangian “engineering” mostly driven by the formal search for the desired result. This conceptual framework looks promising

30. TeVPA08 Beijing -24 September 2008 3030 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, arXiv:0801.1921, to appear on Int. Jour. Mod. Phys. D arXiv:0801.1921

31. TeVPA08 Beijing -24 September 2008 31 VII Friedmann Seminar João Pessoa 1 July 2008 31

32. TeVPA08 Beijing -24 September 2008 3232 …. 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. The idea of motion may not be applied to it. Albert Einstein, Leiden, 1920 Ether again

33. TeVPA08 Beijing -24 September 2008 3333 Some history “Ether is a very wonderful thing. It may exist only in the imagination of the wise, being invented and endowed with properties to suit their hypotheses; but we cannot do without it. How is energy to be transmitted through space without a medium?” Oliver Heaviside, Electrical Papers, 1892

34. TeVPA08 Beijing -24 September 2008 3434 The introduction of a “luminiferous ether” will prove to be superfluous inasmuch as the view here to be developed will not require an “absolutely stationary space”….. Albert Einstein, 1905 Ether is superfluous

35. TeVPA08 Beijing -24 September 2008 3535 The cosmological constant “Much later, when I was discussing cosmological problems with Einstein, he remarked that the introduction of the cosmological term was the biggest blunder of his life. ----” George Gamow, My World Line, 1970