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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

Large-scale Peculiar Motions & Apparent Cosmic Acceleration

NEB XIV, Ioannina, June 2010

Christos Tsagas

AU Thessaloniki

drifting observers 1
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).
drifting observers 2
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 .
average peculiar kinematics
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.
the raychaudhuri equations
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 .
the deceleration parameters
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).

apparent acceleration 1
Apparent acceleration (1)
  • To linear order in υa,

.

  • Then, is compatible with when

.

  • Possibility for (local) apparent acceleration.
apparent acceleration 2
Apparent acceleration (2)

In an almost-FRW spacetime with p=0 and ϑ<Θ.

A: region with (faster expansion).

B: region with (apparent acceleration).

acceleration from deceleration
Acceleration from deceleration
  • To linear order in υa,

,

with .

  • Then, .
  • Thus, is compatible with .
weak strong acceleration
Weak & strong acceleration
  • Weakly accelerated expansion:

.

  • Strongly accelerated expansion:

.

  • The SN data seem to suggest weak acceleration.
conditions for acceleration
Conditions for acceleration
  • Are there fast enough peculiar velocities to make

work? Maybe, after Watkins etal & Kashlinsky etal.

  • Simplest case when . Then, when:
  • .
examples
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).

examples13
Examples
  • For , we have apparent acceleration ( ) if

when , or if

when .

summary
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.