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Accelerating Expansion from Inhomogeneities ?

Accelerating Expansion from Inhomogeneities ?. Je-An Gu ( 顧哲安 ) National Taiwan University. Collaborators: Chia-Hsun Chuang ( 莊家勛 ) W-Y. P. Hwang ( 黃偉彥 ). (astro-ph/0512651). IoPAS 2006/03/17. Acceleration Expansion. Based on FRW Cosmology.

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Accelerating Expansion from Inhomogeneities ?

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  1. Accelerating Expansion from Inhomogeneities ? Je-An Gu(顧哲安) National Taiwan University Collaborators: Chia-Hsun Chuang (莊家勛) W-Y. P. Hwang (黃偉彥) (astro-ph/0512651) IoPAS 2006/03/17

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

  3. Supernova data ? Cosmic Acceleration  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 ? Based on FRW Cosmology (homogeneous & isotropic)

  4. Einstein equations satisfy Einstein equations BUT in general DONOT.

  5. Questions Supernova data ? Cosmic Acceleration Cosmic Acceleration requires Dark Energy?

  6. 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?

  7. 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.

  8. What is Accelerating Expansion ? (I) Line Acceleration What is Accelerating Expansion ? (II) Domain Acceleration Lemaitre-Tolman-Bondi (LTB) Solution (exact solution in GR) (spherically symmetric dust fluid)

  9. 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.

  10. 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)

  11. 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)

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

  13. 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

  14. 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)

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

  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=3 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. Domain Acceleration : qD < 0 k(r) tb(r) arbitrary functions of r : k(r) , 0(r) , tb(r)  tb(r) = 0 :NOacceleration [Nambu and Tanimoto: incorrect example.]   parameters : (nk, kh, rk), (nt, tbh, rt), 0 , rD , t

  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 k(r) = 0 at r = 0.82 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. Summary and Discussions  Against the common intuition and consensus : normal matter  attractive gravity  deceleration, Counter-examples for both the Line and the Domain Acceleration are found. • These examples support : Inhomogeneity Acceleration • These examples raise two issues : (next slide)

  36. How to understand the examples ? (GR issue) Can Inhomog. explain “Cosmic Acceleration”? (Cosmology issue)

  37. Can Inhomog. explain “Cosmic Acceleration”? ? SN Ia Data Cosmic Acceleration Mathematically, possible. In Reality?? ? ? Inhomogeneities Can Inhomogeneities explain SN Ia Data? IF YES Do these Inhomog. Indicate Cosmic Acceleration?

  38. Can Inhomogeneities explain SN Ia Data ? under-density over-density LTB LTB LTB LTB source LTB LTB LTB earth (Each circle represents a LTB region.)

  39. Can Inhomogeneities explain SN Ia Data ? light (No matter whether inhomogeneities can solely explain SN Ia data, …) The effects of inhomogeneities on the cosmic evolution should be restudied. energy density (x) x

  40. 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 !?

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

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