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Large-scale Peculiar Motions & Apparent Cosmic Acceleration

Large-scale Peculiar Motions & Apparent Cosmic Acceleration. NEB XIV, Ioannina, June 20 1 0. Christos Tsagas AU Thessaloniki. Drifting observers (1). The CMB frame defines and measures peculiar velocities: ũ a = γ ( u a + υ a ) ,

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Large-scale Peculiar Motions & Apparent Cosmic Acceleration

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  1. Large-scale Peculiar Motions & Apparent Cosmic Acceleration NEB XIV, Ioannina, June 2010 Christos Tsagas AU Thessaloniki

  2. Drifting observers (1) • The CMB frame defines and measures peculiar velocities: ũa=γ(ua+υa), where γ2=√1-υ2 and uaυa=0 (with υ2«1 always). • Assume a dust-dominated FRW universe (relative to ua).

  3. Drifting observers (2) • Observers have their own time and 3-D space • Time directions: along and . • 3-D metrics: and . • Time derivatives: and . • 3-D derivatives: and .

  4. Average peculiar kinematics • Average motion determined by the volume scalars: (for the CMB frame). (for the drifting frame). (for the peculiar flow). • When υ2≪1, , • Here, ϑ>0 and ϑ<Θ.

  5. The Raychaudhuri equations • Generally: , with ρ: density, p: pressure, σ: shear, ω: vorticity & Aa: 4-acceleration. • In the CMB frame: . • In the drifting frame: (to first order in υa). • Also to first order in υa: and .

  6. The deceleration parameters • Generally: , • In the CMB and the drifting frames: and . • Then, Raychaudhuri’s equations read: (in the CMB frame). and (in the drifting frame).

  7. Apparent acceleration (1) • To linear order in υa, . • Then, is compatible with when . • Possibility for (local) apparent acceleration.

  8. Apparent acceleration (2) In an almost-FRW spacetime with p=0 and ϑ<Θ. A: region with (faster expansion). B: region with (apparent acceleration).

  9. Acceleration from deceleration • To linear order in υa, , with . • Then, . • Thus, is compatible with .

  10. Weak & strong acceleration • Weakly accelerated expansion: . • Strongly accelerated expansion: . • The SN data seem to suggest weak acceleration.

  11. Conditions for acceleration • Are there fast enough peculiar velocities to make work? Maybe, after Watkins etal & Kashlinsky etal. • Simplest case when . Then, when: • .

  12. Examples • Ω=1: Then, when ϑ/Θ>1/6. • Ω=1/2: Then, when ϑ/Θ>1/10. ∼30 Mpc - ∼60 Mpc (Li and Schwarz), ∼100 Mpc (Kashlinsky etal). • Ω=1/10: Then, when ϑ/Θ>1/42. up to ∼600 Mpc (Kashlinsky etal).

  13. Examples • For , we have apparent acceleration ( ) if when , or if when .

  14. Summary • Locally accelerated expansion is, in principle, possible in linearly perturbed FRW models with conventional matter. • The effect of peculiar motions probably consistent with some degree of (dipole) anisotropy in the distribution of q.

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