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Accelerating Expansion from Inhomogeneities ?

Accelerating Expansion from Inhomogeneities ?. Je-An Gu (National Taiwan University). Collaborators: Chia-Hsun Chuang. (astro-ph/0512651). IRGAC2006, 2006/07/14. Accelerating Expansion. Based on FRW Cosmology. (homogeneous & isotropic). Supernova data  ?  Cosmic Acceleration.

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Accelerating Expansion from Inhomogeneities ?

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  1. Accelerating Expansion from Inhomogeneities ? Je-An Gu (National Taiwan University) Collaborators: Chia-Hsun Chuang (astro-ph/0512651) IRGAC2006, 2006/07/14

  2. Accelerating Expansion Based on FRW Cosmology (homogeneous & isotropic)

  3. Supernova data ? Cosmic Acceleration Based on FRW Cosmology (homogeneous & isotropic)  However, apparently, our universe is NOT homogeneous & isotropic.  At large scales, after averaging, the universe IS homogeneous & isotropic.  But, averaging!? Is it legal ? Does it make sense ? •  Existence of cosmic acceleration • Dark energy as a necessity of understanding acceleration

  4. Einstein equations For which satisfy Einstein equations, in general DONOT.

  5. Dark Geometry Effects of Inhomogeneities through averaging Einstein equations Toy Model: ds2= dt2 a2(1 + h coskx cosky coskz) (dx2+ dy2+ dz2) Einstein equations after averaging in space: (perturb: h << 1) eff peff =  eff / 3 peff

  6. Questions Supernova data ? Cosmic Acceleration Cosmic Acceleration requires Dark Energy? (or Inhomogeneity-induced Acceleration ?)

  7. Cosmic Acceleration requires Dark Energy? Common Intuition / Consensus Normal matter  attractive gravity  slow down the expansion Need something abnormal : e.g. cosmological constant, dark energy -- providing anti-gravity (repulsive gravity) Is This True?

  8. Is This True ? Intuitively, YES!(of course !!) Mission Impossible ? orMission Difficult ? This is what we did. Normal matter  attractive gravity  slow down the expansion Common Intuition / Consensus ** Kolb, Matarrese, and Riotto (astro-ph/0506534) : Inhomogeneities of the universe might induce acceleration. • Two directions: • Prove NO-GO theorem. • Find counter-examples. We found counter-examples for a dust universe of spherical symmetry, described by the Lemaitre-Tolman-Bondi (LTB) solution.

  9. Lemaitre-Tolman-Bondi (LTB) Solution (exact solution in GR) (unit: c = 8G = 1) Dust Fluid + Spherical Symmetry k(r) = const., 0(r) = const., a(t,r) = a(t)  FRW cosmology Solution (parametric form with the help of ) arbitrary functions of r : k(r) , 0(r) , tb(r)

  10. Line (Radial) Acceleration ( qL < 0 ) Radial: Inhomogeneity  Acceleration Angular : No Inhomogeneity  No Acceleration

  11. What is Accelerating Expansion ? (I) homogeneous & isotropic universe: RW metric: Line Acceleration L We found examples of qL < 0 (acceleration) in a dust universe described by the LTB solution.

  12. Line (Radial) Acceleration : qL < 0 k(r) 1 rk 0 r kh arbitrary functions of r : k(r) , 0(r) , tb(r) Inhomogeneity  the less smoother, the better  parameters : (nk, kh, rk) , 0 , rL , t

  13. Examples of Line (Radial) Acceleration : qL < 0 1 k(r) r rk 0 kh arbitrary functions of r : k(r) , 0(r) , tb(r) parameters : (nk, kh, rk) , 0 , rL , t Acceleration Observations  q ~ 1 (based on FRW cosmology)

  14. Examples of Line (Radial) Acceleration : qL < 0 k(r) = 0 at rk = 0.7 Over-density Under-density

  15. Examples of Line (Radial) Acceleration : qL < 0 k(r) = 0 at rk = 0.7 characterizing the accel/deceleration status of the radial line elements

  16. Examples of Line (Radial) Acceleration : qL < 0 k(r) = 0 at rk = 0.7 Acceleration Deceleration Deceleration

  17. Examples of Line (Radial) Acceleration : qL < 0

  18. Examples of Line (Radial) Acceleration : qL < 0 Inhomogeneity Acceleration

  19. Examples of Line (Radial) Acceleration : qL < 0 1 k(r) r rK 0 nk=5 kh Easy to generate larger nk larger inhomogeneity Deceleration Acceleration

  20. Examples of Line (Radial) Acceleration : qL < 0 Deceleration Acceleration

  21. r = rD spherical domain r = 0 Domain Acceleration ( qD < 0 )

  22. What is Accelerating Expansion ? (II) We found examples of qD < 0 (acceleration) in a dust universe described by the LTB solution. [Nambu and Tanimoto (gr-qc/0507057) : incorrect example.] Domain Acceleration a large domain D (e.g. size ~ H01) Volume VD NO-GOqD 0 > 0 (deceleration) in a dust universe (see, e.g., Giovannini, hep-th/0505222)

  23. Examples of Domain Acceleration : qD < 0 k(r) tb(r) arbitrary functions of r : k(r) , 0(r) , tb(r) parameters : (nk, kh, rk), (nt, tbh, rt), 0 , rD , t Acceleration

  24. Examples of Domain Acceleration : qD < 0 k(r) = 0 at r = 0.82 Over-density Under-density

  25. Examples of Domain Acceleration : qD < 0 characterizing the accel/deceleration status of the radial line elements Acceleration Deceleration Deceleration

  26. Examples of Domain Acceleration : qD < 0 Acceleration

  27. Examples of Domain Acceleration : qD < 0 Deceleration Acceleration

  28. Examples of Domain Acceleration : qD < 0 Deceleration Acceleration

  29. Examples of Domain Acceleration : qD < 0 larger nt larger inhomogeneity tb(r) Deceleration Acceleration

  30. Examples of Domain Acceleration : qD < 0 Deceleration Acceleration

  31. Examples of Domain Acceleration : qD < 0 Acceleration

  32. Examples of Domain Acceleration : qD < 0 Deceleration Acceleration

  33. Examples of Domain Acceleration : qD < 0 Deceleration Acceleration

  34. Summary and Discussions

  35. Model: Inhomogeneous Universe (Reality?) ? ? • These examples raise two issues : Can inhomogeneities explain cosmic acceleration ? (cosmology issue) How to understand these counter-intuitive examples ? (GR issue)  Toy Model: ds2= dt2 a2(1 + h coskx cosky coskz)(dx2+ dy2+ dz2) peff =  eff / 3  Against the common intuition and consensus : normal matter  attractive gravity  deceleration, Counter-examples (acceleration) are found. • These examples support : Inhomogeneity Acceleration

  36. Can Inhomog. explain “Cosmic Acceleration”? IF YES Does Cosmic Acceleration exist? ? SN Ia Data Cosmic Acceleration Mathematically, possible. In Reality?? ? ? Inhomogeneities Can Inhomogeneities explain SN Ia Data?

  37. How to understand the examples ? Intuition from Newtonian gravity, not from GR. (valid only for … ?) (x) Newton?NO. GR?YES. Common Intuition / Consensus Normal matter  attractive gravity  slow down the expansion Intuition for GR ?NO !?

  38. Summary and Discussions GR is still not fully understood after 90 years !!

  39. Line (Radial) Acceleration : qL < 0 1 k(r) r rK 0 Sharp enough change in kh(r) kh ( For constant 0 ) Sufficient and Necessary Condition: Tuning/choosing the boundary condition

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