Small-scale angular fluctuations in the microwave background radiation and the existence of isolated large-scale structures in the universe

Abstract

The relative fluctuation of the present temperature associated with the microwave background radiation (MBR) on a small angular scale, (deltaT/T)/sub 0/, can be related for a general inhomogeneous cosmological model to the kinematical quantities, their gradients, and the Weyl tensor through the geodesic deviation equation. We apply this result to calculate the induction of temperature fluctuations in the MBR by a spherically symmetric cluster (or void) of matter or radiation or both, considered as a perturbation in a flat Friedmann universe, with negligible pressure. For an isolated object (void or cluster) with radius roughly-equal10/sup 3/h/sup -1/ Mpc and located outside our present horizon, we have found, taking into account recent data on the anisotropies of the MBR at an angular scale 6/sup 0/, that the relative mass fluctuation is bounded by deltaVertical BarM/MVertical Bar< or approx. =10%. On the other hand, if we are near the cluster (or void) center (radius of the object roughly-equal6 x 10/sup 2/h/sup -1/ Mpc and distance from the observer to the center approx. =10h/sup -1/ Mpc), the observational angular fluctuations of the MBR imply that deltaVertical BarM/MVertical Bar< or approx. =10%.