1. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 1 Fitting the luminosity data from type Ia supernovae by means of the cosmic defect theory Angelo Tartaglia DIFIS – Politecnico and INFN Torino, Italy

2. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 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 Defects and Vector Theories: general Lagrangians Defects and Vector Theories: general Lagrangians Open problems Open problems

3. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 3 The accelerated expansion (luminosity data of SnIa’s)

4. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 4 The power spectrum of CMB k=0

5. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 5 Presently agreed expansion

6. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 6 Einstein equations Spacetime geometry“Matter” Why is Λ on the left?

7. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 7 Something missing Inflation Gravity in clusters and galaxies Accelerated expansion There is something missing Modify GR Introduce the missing entities Give up GR and look for another theory

8. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 8 Accept a four- (N-) dimentional spacetime manifold Add “matter” components Isotropy and homogeneity Perfect fluid

9. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 9 Λ Cold Dark Matter Simplest and most effective model for the universe; however: “matter” must be 7 times what we “see” (~30% of the source); Λ corresponds to 70% of the souce but … what is Λ?

10. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 10 Trying a new approach: The Cosmic Defect theory Motivation, besides the simple fitting of the data: describing the large scale behaviour of the universe in terms of intrinsic properties of a four-dimensional continuum; interpreting space-time as Einstein’s GR ether ether

11. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 11 Strain in a continuum N-dimensional “sheet” Strain induced by boundary conditions

12. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 12 A defect Internal “spontaneous” strain state

13. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 13 Four-dimensional point defect

14. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 14 Geometry, elasticity and defects

15. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 15 In a strained medium each point is in one to one correspondence with points in the unstrained state The new situation is diffeomorphic to the old one ξ is a function of x Intrinsic coordinatesExtrinsic coord. Displacement

16. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 16 Induced metric Strain tensor

17. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 17 “Radial” displacement field (space isotropy and homogeneity)

18. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 18 The line element Unperturbed Strained

19. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 19 A Robertson-Walker universe

20. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 20 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

21. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 21 Phase space analogy FRW universe Inertial expansion Accelerated expansion Decelerated expansion Point particle Free motion Driving force Braking force

22. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 22 A simple classical problem Motion of a point massive particle in a viscous medium

23. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 23 Invariant formulation of the same problem

24. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 24 Spacetime “Dissipative” action integral Same structure as in the classical simple case The “viscous” properties of space-time are contained in the vector field 

25. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 25 Robertson Walker symmetry Isotropy and homogeneity in 3 dimensions RW line element The symmetry is induced by the presence of a “defect”

26. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 26 Impose the 4-isotropy around the origin and use cosmic time as the “radial” coordinate

27. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 27 Symmetry and application of the minimal action principle do not commute Defect means Symmetry first

28. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 28 Non-trivial if Lagrangian

29. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 29 Divergence free vector vector

30. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 30 The expansion rate ( a and time in units of Q ) Choose the + sign

31. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 31 Expansion rate Accelerated expansion Asymptotic stop

32. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 32 Expansion versus cosmic time Inflation Acceleration

33. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 33 Fitting the data from SnIa SnIa

34. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 34 The distance modulus

35. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 35 The energy function for the CD theory

36. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 36 Multicomponent cosmic fluid Equation of state Conservation law Expansion rate

37. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 37 Fitting the data (192 SnIa)

38. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 38 ΛCDM  2 = 1.029 CD  2 = 1.092 Reduced  2 of the fits

39. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 39 The Hubble parameter H 0 = (62.8 ± 1.7) km/s  Mpc Most models ~64 km/s  Mpc Observation~75 km/s  Mpc

40. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 40 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 inflation is too strong and long lasting (troubles with nucleosynthesis and formation of structures) The inflation is too strong and long lasting (troubles with nucleosynthesis and formation of structures) The exponential in the action integral is a poweful multiplier, but it should be weakened The exponential in the action integral is a poweful multiplier, but it should be weakened

41. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 41 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. Once it has been induced, the γ vector has its own dynamics and energy content which must be taken into account Once it has been induced, the γ vector has its own dynamics and energy content which must be taken into account

42. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 42 General Lagrangian treatment (non-exponential coupling) Non-minimal coupling

43. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 43 The equations for a and 

44. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 44 Special or trivial solutions Matter dominated FRW

45. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 45 Correspondences Bimetric theories: “pre-shaped container” Bimetric theories: “pre-shaped container” Vector-tensor theories Vector-tensor theories Curvature fluid Curvature fluid

46. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 46 Final remarks The CD theory provides a consistent physical interpretation of space-time giving a heuristic tool to move across the Lagrangian “engineering” mostly driven by the formal search for the desired result. This conceptual framework looks promising

47. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 47 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

48. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 48 Thank you

49. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 49 Why SnIa? Accreting white dwarf Supernova explosion Tycho Brahé 1572 (Chandra’s image)

50. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 50 SnIa is a good candle Stable light curvecurve

51. 5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 2008 51 …. according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether. According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. 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.it Albert Einstein, Leiden, 1920 Ether again