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

TeVPA08 Beijing -24 September 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

TeVPA08 Beijing -24 September 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

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

TeVPA08 Beijing -24 September 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?

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

TeVPA08 Beijing -24 September A defect Internal “spontaneous” strain state

TeVPA08 Beijing -24 September Geometry, elasticity and defects Reference manifold Natural manifold

TeVPA08 Beijing -24 September 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

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

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

TeVPA08 Beijing -24 September A Robertson-Walker universe

TeVPA08 Beijing -24 September 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

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

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

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

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

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

TeVPA08 Beijing -24 September Divergence free vector

TeVPA08 Beijing -24 September Expansion rate Accelerated expansion Asymptotic stop

TeVPA08 Beijing -24 September Expansion versus cosmic time Inflation Acceleration

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

TeVPA08 Beijing -24 September Distance modulus vs z (192 SnIa)

TeVPA08 Beijing -24 September ΛCDM  2 = CD  2 = Reduced  2 of the fits

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

TeVPA08 Beijing -24 September 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?

TeVPA08 Beijing -24 September 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.

TeVPA08 Beijing -24 September 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

TeVPA08 Beijing -24 September 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

TeVPA08 Beijing -24 September 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:

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

TeVPA08 Beijing -24 September …. 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

TeVPA08 Beijing -24 September 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

TeVPA08 Beijing -24 September 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

TeVPA08 Beijing -24 September 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