DENSITY CONTRAST-PECULIAR VELOCITY RELATION IN THE NEWTONIAN GAUGE

Abstract

We investigate relation between density contrast and peculiar velocity in the Newtonian gauge, in general relativistic framework of theory of large scale structure formation in the universe. According to the gauge-invariant property of the energy-momentum tensor in this gauge, the velocity perturbation behaves like the Newtonian peculiar velocity. In this framework, the relation between peculiar velocity and density contrast with respect to the Newtonian–Peebles formula has an extra correction term which is ignorable for the small scale structures. The relativistic correction of peculiar velocity for structures of the extent of hundred mega parsec is about few percents which is smaller than the accuracy of the recent peculiar velocity measurements. We also study CMB anisotropies due to the Doppler effect in the Newtonian gauge compared with those obtained using Newtonian gravity.