Peculiar velocities of nonlinear structure: Voids in McVittie spacetime

As a study of peculiar velocities of nonlinear structure, we analyze the model of a relativistic thin-shell void in the expanding universe. First, adopting McVittie (MV) spacetime as a background universe, we investigate the dynamics of an uncompensated void with negative MV mass. Although the motion itself is quite different from that of a compensated void, as shown by Haines & Harris, the present peculiar velocities are not affected by MV mass. Second, we discuss how precisely the formula in the linear perturbation theory applies to nonlinear relativistic voids, using the results of our first investigation as well as previous results for the homogeneous background (Sakai, Maeda, & Sato). Third, we reexamine the effect of the cosmic microwave background radiation. Contrary to the results of Pim & Lake, we find that the effect is negligible. We show that their results are due to inappropriate initial conditions. Our results in the three parts of our study suggest that the formula in the linear perturbation theory is approximately valid even for nonlinear voids.