Friday, June 28, 2013

1306.6501 (Christos G. Tsagas et al.)

The peculiar Raychaudhuri equation    [PDF]

Christos G. Tsagas, Miltiadis I. Kadiltzoglou
Peculiar motions are commonplace in the universe. Our local group of galaxies, for example, drifts relative to the Hubble flow at about 600 km/sec. Such bulk flows are believed to fade away as we move on to progressively larger scales. Recently, however, there have been reports of peculiar motions larger and faster than typically expected. If these claims are correct, the role of peculiar flows in shaping the kinematics of our universe has been probably underestimated. Here, we use general relativistic techniques to analyse the average kinematics of large-scale bulk motions and compute the nonlinear Raychaudhuri equation of such flows. In doing so, we introduce two families of observers. One at rest with the Hubble expansion and another following the peculiar motion. We first derive the fully nonlinear expressions of the "peculiar" Raychaudhuri equation in both frames and identify a range of relative motion effects. Linearised around a Friedmann universe with conventional pressureless dust, the full equations reduce to a simple relation with no explicit contribution from the matter component of the universe. Using cosmological perturbation theory, we obtain alternative forms for the aforementioned linear expression of Raychaudhuri's formula. These are generally scale dependent and incorporate the effects of inhomogeneities. Overall, the structure of the "peculiar" Raychaudhuri equation suggests that, even at the linear level, the average kinematics of large-scale bulk motions is more complex than generally anticipated.
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