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非各向同性宇宙与 Finsler 时空

非各向同性宇宙与 Finsler 时空. 常哲 中国科学院高能物理研究所 2015.11.24 合肥. The basic premise of general relativity: the correct way to account for the acceleration of objects due to gravity is to consider spacetime to be curved in the presence of matter and energy. The four key observational successes of the

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非各向同性宇宙与 Finsler 时空

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  1. 非各向同性宇宙与Finsler时空 常哲 中国科学院高能物理研究所 2015.11.24 合肥

  2. The basic premise of general relativity: the correct way to account for the acceleration of objects due to gravity is to consider spacetime to be curved in the presence of matter and energy.

  3. The four key observational successes of the standard Hot Big Bang model • Expansion of the Universe • Origin of the cosmic background radiation • Nucleosynthesis of the light elements • Formation of galaxies and large-scale structure The Big Bang model makes accurate and scientifically testable hypotheses in each of these areas and the remarkable agreement with the observational data gives us considerable confidence in the model.

  4. Supernova Cosmology Project Supernovae are one of the most energetic explosions in nature, making them like a 1028megaton bomb (i.e., a few octillion nuclear warheads).

  5. The Wilkinson Microwave Anisotropy Probe David Wilkinson The science goals: relative CMB temperature be measured accurately over the full sky with high angular resolution and sensitivity. over the full sky with an angular resolution of at least 0.3° a sensitivity of 20 µK per 0.3° square pixel with systematic artifacts limited to 5 µK per pixel. WMAP Mission

  6. June 30, 2001WMAP Launch15:46:46 EDT on June 30, 2001 aboard a Delta II-7425-10 (no. 286) launch vehicle.Oct. 1, 2001WMAP Arrives at L2Following a three month journey, WMAP arrived safely at its permanent observing station near the L2 Lagrange Point, a quasi-stable position 1.5 million km from Earth in the direction opposite the Sun.April 2002WMAP Covers the Full SkyWMAP completed its first full sky observations.

  7. Planck shows almost perfect cosmos – plus axis of evil

  8. Hemispherical asymmetry in CMB Planck satellite

  9. Cosmological expansion rate in different direction is not the same Antoniou, I. & Perivolaropoulos, L., JCAP 12, 1475 (2010). Maximum: \Omega_m0=0.30 Minimum: \Omega_m0=0.19

  10. Spatial variation of fine structure constant

  11. ICM Gas (X-ray) Bullet Cluster: baryonic mass center separates from gravitational center Galaxies 83% 17% Convergence (Lensing) Image provided courtesy of Chandra X-ray Observatory

  12. Finsler geometry In 1854 Riemann saw the difference between the quadratic differential form--Riemannian geometry and the general case. The study of the metric which is the Fourth root of a quartic differential form is quite time--consuming and does not throw new light to the problem." Happily, interest in the general case was revived in 1918 by Paul Finsler's thesis, written under the direction of Caratheodory.

  13. What if Riemann Geometry Finsler Geometry ？

  14. Finsler structure of M . with the following properties: • Regularity: F is C on the entire slit tangent bundle TM\ 0 (ii) Positive homogeneity : F(x,  y)=  F(x,y), for all  >0 (iii) Strong convexity: the Hessian matrix Is positive-definite at every point of TM\0

  15. The symmetric Cartan tensor Cartan tensor Aijk=0 if and only if gij has no y-dependence A measurement of deviation from Riemannian Manifold

  16. Chern Theorem guarantees the uniqueness of Chern connection. S. S. Chern, Sci. Rep. Nat. Tsing Hua Univ. Ser. A 5, 95 (1948); or Selected Papers, vol. II, 194, Springer 1989. Torsion freeness Almost g-compatibility

  17. Torsion freeness is equivalent to the absence of dyiterms in ij together with the symmetry Almost g-compatibility implies that where

  18. Curvature The curvature 2-forms of Chern connection are The expressionof ijin terms of the natural basis is of the form where R, P and Q are the hh-, hv-, vv-curvature tensors of the Chern connection, respectively.

  19. Gravity and large scale structure The tangent spaces (TxM, Fx) of an arbitrary Finsler manifolds typically not isometric to each other. Given a Berwald space, all its tangent spaces are linearly isometric to a common Minkowski space A Finsler structure F is said to be of Berwald type if the Chern connection coefficients ijk in natural coordinates have no y dependence. A direct proposition on Berwald space is that hv--part of the Chern curvature vanishes identically

  20. Gravitational field equation on Berwald space X. Li and Z. Chang, Toward a Gravitation Theory in Berwald--Finsler Space ,gr-qc/0711.1934.

  21. Possible model of accelerated expanding Universe Z. Chang and X. Li, Robertson-Walker metric satisfies the requirements of homogeneity, isotropy and closure Modified Friedmann model in Randers-Finsler space of approximate Berwald type as a possible alternative to dark energy hypothesis, Phys. Lett. B676 (2009) 173, arXiv 0901.1023

  22. Ricci tensor By making use of the energy-momentum tensor, the Einstein equation reads Time-time component: Space-space components: The space-time components give 0=0 Friedmann equation

  23. The Randers-Finsler metric The Friedmann equation Let to be the Robertson-Walker type

  24. Omitting the O(b2) term and combining with the the space-space component of the field equations, we obtain One can see clearly that the accelerated expanding universe is guaranteed by the constraint

  25. So that the complete constraint on Randers-Finsler structure to support accelerated expanding universe is It means that a negative provides an effective repulsive force in the course of universe expanding.

  26. Convergence MOND Quadrupole Dipole + Quadrupole X. Li, M.-H. Li*, H.-N. Lin, and Z. Chang, Mon. Not. Roy. Astron. Soc. 428, 2939 (2012).

  27. Convergence X. Li, M.-H. Li*, H.-N. Lin, and Z. Chang, Mon. Not. Roy. Astron. Soc. 428, 2939 (2012).

  28. Preferred direction in Riemann spacetime • Metric • Luminosity distance Z. Chang, M. H. Li and S. Wang , Phys. Lett. B737 (2013) 257. Z. Chang, M. H. Li, X. Li, and S. Wang, Eur. Phys. J. C73 (3013) 2459.

  29. Omega_m=0.27, H_0=70, • A=(-2.34+-0.91)*10^-5

  30. CMB温度涨落之半球不对称 Z. Chang, and S. Wang, Eur.Phys.J. C73 (2013) 2516 • 暴胀宇宙为Randers时空： 取 为Friedmann-Robertson-Walker度规 设 为类时矢量： • 在暴胀子场的推动下，Einstein引力场方程存在暴胀解： 宇宙学演化 CMB温度涨落的幅值（在ɭ≤60的大尺度上）在天空的一边比相对的一边要大 Planck2013结果

  31. 暴胀子场扰动的Fourier模式满足运动方程 • 曲率扰动原初功率谱 • 结论及意义： 1. 在Finsler时空中“首次”实现（空间）各向异性的暴胀； 2.Finsler几何能够导致（统计学）各向异性的原初功率谱； 3.Randers-Finsler暴胀宇宙可以解释半球不对称反常，与WMAP和Planck的观测一致。

  32. Conlusions • We can setup a General relativity in Finsler spacetime • Finsler geometry may really supply a framework of astronomy and cosmology without invoking dark matter and dark energy hypothesis. • Finsler geometry is a natural framework for describing an anisotropic spacetime

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