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

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

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

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

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

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

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

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

5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May 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?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

5th Italian-Sino Workshop on Relativistic Astrophysics Taipei - Hualien 29 May A. Tartaglia, M. Capone, Int. Jour. Mod. Phys. D, 17, (2008) A. Tartaglia, N. Radicella, Phys. Rev. D, 76, (2007) A. Tartaglia, M. Capone, V. Cardone, N. Radicella, arXiv: , to appear on Int. Jour. Mod. Phys. D arXiv:

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

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

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

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