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R98222063 Pao -Yu Wang 王寶瑜

Cosmology Final Report: Dark energy and the mass of galaxy clusters C. Bambi, Phys . Rev. D 75 : 083003,2007, arXiv:0703645. R98222063 Pao -Yu Wang 王寶瑜. Outline. Introduction of the idea of this paper The role of cosmological constant Different proposals for accelerating universe

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R98222063 Pao -Yu Wang 王寶瑜

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  1. Cosmology Final Report:Dark energy and the mass of galaxy clustersC. Bambi, Phys. Rev. D 75:083003,2007, arXiv:0703645 R98222063 Pao-Yu Wang 王寶瑜

  2. Outline • Introduction of the idea of this paper • The role of cosmological constant • Different proposals for accelerating universe • Dark energy as cosmological constant • Behavior and effect in smaller scale • Detection of galaxy cluster • Possible ways to distinguish different model • Problem in gravitational lensing

  3. Introduction of this paper • “Dark Energy and the mass of Galaxy Clusters” • Cosimo Bambi, Phys. Rev. D 75:083003,2007, arXiv:0703645 • Main idea: • Current dark energy observation are based on very large scale • Can not distinguish different DE model • Proposed a possible way to probe DE at small scale

  4. Review of Λ in general relativity • To solve the “non-static” problem • Einstein tried to get a static solution • Directly solving (with FRW metric) leads to: , • But for k=1 , da/dt =0 & nonnegative pressure, will never be 0!

  5. Review of Λ in general relativity • People don’t know expansion of universe yet • Einstein:  in this way for a positive Λ , the universe can be static • Then Hubble discover the expansion of the universe • The addition of Λ is not illegal • Starts to be interpreted with different meanings Ex:Vacuum energy

  6. Accelerating Universe • Dark Energy as cosmological constant • Vacuum energy , universal • Dynamical dark energy • Geometric dark energy – or Modify gravity • Accelerating without dark energy • Back-reaction perturbations

  7. Dark Energy as Cosmological Constant • Use Schwarzschild-de Sitter metric: • Solve geodesic EQ with Newtonian limit: We get and An object at radius r “feels” Meff Standard Newtonian mechanics

  8. Dark Energy as Cosmological Constant • Λ serves as a repulsive force • For Milky Way, M~1012 M, at r ~1.2 Mpc • Meff=0 So the sphere inside 1.2Mpc is a bound system • inside: attractive outside: repulsive Bubbles or Vacuole: Repel if no contact!

  9. Galaxy cluster mass • Galaxy clusters: largest bound system • Above effect can affect dynamics of these bound system • Important to study the mass of galaxy clusters • Estimating cluster mass: • Kinematical dynamics: detect Meff • X-ray from intracluster gas, but potential is related to Meff again • Gravitational lensing!!

  10. Gravitational lensing • As in this paper (and some others), lensing is claimed to be independent from Λ • Λ dropped out when computing lensing eq. • But at about the same year: • Other people suggest Λ dependence!! • Reason (argument): Λdrop out in lensing eq. But light ray travel through the geometry, Λ reappears

  11. Conclusion • Dark energy models needs a better way to distinguish from each other • If Λ is indeed inhomogeneous, then small scale observation is needed • Have to choose a suitable scale, not too small nor too big • Gravitational lensing may still be affected by Λ, • Needs to be modified

  12. Thanks for listening!

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