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

May 28, 2010, Dezhou Two geometrical quantities Torsion cosmology Fit SNeIa Analytical solutions of late-time in torsion cosmology Summary Contents 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 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 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.

Metric-compatible connection 1-form Orthonormal coframe 1-form Metric May 28, 2010, Dezhou

Pioneer Elie Joseph Cartan ( ) 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 strong weak electromagnetic gravity can be described by local gauge theory. Poincaré Gauge Theorygravity Torsion Cosmology Poincare gauge theory

May 28, 2010, Dezhou 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 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. Scalar modes

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

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

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

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

May 28, 2010, Dezhou The Discovery Data

May 28, 2010, Dezhou In our model, the luminosity distance is Fit SNIa For comparison with ΛCDM model: Ω M = 0.3, Ω Λ = 0.3 and χ 2 = 177, χ 2 /157 = The best fit for the torsion for the torsion parameters (a2, b) of the model are found by minimizing the quantity

May 28, 2010, Dezhou

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

Solutions with constant scalar curvature We consider the scalar curvature is constant as follows:

May 28, 2010, Dezhou Solution II When

May 28, 2010, Dezhou Solution III When

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

May 28, 2010, Dezhou Bifurcation

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

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

May 28, 2010, Dezhou

 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. Summary

May 28, 2010, Dezhou Thanks!