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A Realistic Torsion Cosmological Model

A Realistic Torsion Cosmological Model. Li Xin-Zhou Shanghai United Center for Astrophysics, Shanghai Normal University. Contents. Two geometrical quantities Torsion cosmology Fit SNeIa Analytical solutions of late-time in torsion cosmology Summary. Li,Sun and Xi, PRD 79 (2009)

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A Realistic Torsion Cosmological Model

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  1. A Realistic Torsion Cosmological Model Li Xin-Zhou Shanghai United Center for Astrophysics, Shanghai Normal University May 28, 2010, Dezhou

  2. Contents • Two geometrical quantities • Torsion cosmology • Fit SNeIa • Analytical solutions of late-time in torsion cosmology • Summary Li,Sun and Xi, PRD 79 (2009) Li,Sun and Xi, JCAP (2009) Ao,Li and Xi, preprint (2010) Li,Xi and Ao, Preprint (2010) May 28, 2010, Dezhou

  3. Physical / geometrical quantities • In various cosmological models, fundamental quantities are either physical (if they depend upon physical fields) or geometrical (if they are constructed from a spacetime geometry directly). Physical quantities are certainly model-dependent, while geometrical quantities are more universal. • replace physical fields by geometrical quantities in a cosmological theory. May 28, 2010, Dezhou

  4. Two geometrical quantities • Two basic geometrical subjects (tetrad and affine connection) have been discussed widely. Tetrad determines the (symmetric) metric and the local Lorentz frame, while affine connection defines the parallel transport and covariant derivative. • Einstein used (symmetric) metric to establish his General Relativity; • With these two geometrical subjects, we could find a realistic cosmology, in which we don’t have to introduce the mystical dark energy. May 28, 2010, Dezhou

  5. Two 1-forms • Metric-compatible connection 1-form • Orthonormal coframe 1-form • Metric May 28, 2010, Dezhou

  6. Pioneer • Elie Joseph Cartan (1869-1951) • A geometry with an asymmetric Christoffel symbol is said to have torsion. Cartan has incorporated torsion into gravitational theory. • Cartan’s modification of Einstein’s theory attempts to take the spin density of elementary particles as the source of torsion. • A. S. Eddington, Proc.Roy.Soc.Lon.Ser.A99(1921)104 • mentioned the notion of an asymmetry affinf connection in discussing possible extensions of GR May 28, 2010, Dezhou

  7. Poincare gauge theory strong weak can be described by local gauge theory. electromagnetic gravity Poincaré Gauge Theory gravity Torsion Cosmology May 28, 2010, Dezhou

  8. PGT is based on Riemann-Cartan Geometry. It allows for dynamic torsion in addition to curvature. To put gravitation into a gauge theory. The connection dynamics (represented by torsion tensor) decomposes into 6 modes with certain spins and parity: 2±,1±,0±. May 28, 2010, Dezhou

  9. Scalar modes Two “scalar torsion” (0±) may well be the only physically accepted dynamic PGT torsion modes. 0+ or 0- has only a time component,then the homogeneous and isotropic cosmologies are naturally suitable for them. May 28, 2010, Dezhou

  10. “pseudoscalar” 0- have small effects at late time of cosmology evolution, so we do not focus on this mode. “scalar torsion” 0+ can be imagined as having significant magnitude and being dramatically noticed only through the non-linear equations. May 28, 2010, Dezhou

  11. Dynamical equations The torsion and curvature 2-forms are: Which satisfy the Bianchi identities, respectively May 28, 2010, Dezhou

  12. Lagrangiandensity where is the algebraically irreducible parts of the torsion, R is the scalar curvature and E is the pseudoscalar curvature. and are dimensionless parameters, have the same dimension with . May 28, 2010, Dezhou

  13. Dynamical equations For a spatially flat Robertson-Walker cosmological model where we have made the replacement And is Hubble parameter. May 28, 2010, Dezhou

  14. And the energy density of matter component is The Newtonian limit requires . May 28, 2010, Dezhou

  15. Hi z Supernova Team Supernova Cosmology Project Supernova 1998 Two groups May 28, 2010, Dezhou

  16. The Discovery Data May 28, 2010, Dezhou

  17. Fit SNIa In our model, the luminosity distance is The best fit for the torsion for the torsion parameters (a2, b) of the model are found by minimizing the quantity For comparison with ΛCDM model: ΩM = 0.3, Ω Λ = 0.3 and χ2= 177, χ2 /157 = 1.13. May 28, 2010, Dezhou

  18. May 28, 2010, Dezhou

  19. Better model, better fit We have obtained a better fit for our torsion Cosmology! Bao, CMB issues will be considered elsewhere. May 28, 2010, Dezhou

  20. Solutions with constant scalar curvature We consider the scalar curvature is constant as follows: May 28, 2010, Dezhou

  21. Solution II When May 28, 2010, Dezhou

  22. Solution III When May 28, 2010, Dezhou

  23. Fate of universe From the above formula, we get May 28, 2010, Dezhou

  24. Bifurcation May 28, 2010, Dezhou

  25. Solution of non-constant scalar curvature May 28, 2010, Dezhou

  26. We find an approximate formula up to order May 28, 2010, Dezhou

  27. May 28, 2010, Dezhou

  28. Summary • Fit SNeIa We have obtained a better fit for our torsion • Cosmology! • We find three kinds of analytical solutions with a constant affine scalar curvature and a kind of expression with non-constant curvature. In the first case, it is not physical because the matter density will be negative. In the second case, it shows that the dark energy can be mimicked in the torsion cosmological model. In the third case, the charac-teristic of late-time evolution is similar to the universe of matter dominant. In the fourth case, we know the fate of universe that the universe would expand forever, slowly asymtotically to a halt. May 28, 2010, Dezhou

  29. Thanks! May 28, 2010, Dezhou

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