The Evolution of Voids in the Adhesion Approximation

We apply the adhesion approximation to study the formation and evolution of voids in the Universe. Our simulations -- carried out using 128$^3$ particles in a cubical box with side 128 Mpc -- indicate that the void spectrum evolves with time and that the mean void size in the standard COBE-normalised Cold Dark Matter (hereafter CDM) model with $h_{50} = 1,$ scales approximately as $\bar D(z) = {\bar D_0\over \sqrt {1+z}},$ where $\bar D_0 \simeq 10.5$ Mpc. Interestingly, we find a strong correlation between the sizes of voids and the value of the primordial gravitational potential at void centers. This observation could in principle, pave the way towards reconstructing the form of the primordial potential from a knowledge of the observed void spectrum. Studying the void spectrum at different cosmological epochs, for spectra with a built in $k$-space cutoff we find that, the number of voids in a representative volume evolves with time. The mean number of voids first increases until a maximum value is reached (indicating that the formation of cellular structure is complete), and then begins to decrease as clumps and filaments merge leading to hierarchical clustering and the subsequent elimination of small voids. The cosmological epoch characterizing the completion of cellular structure occurs when the length scale going nonlinear approaches the mean distance between peaks of the gravitational potential. A central result of this paper is thatComment: Plain TeX, 38 pages Plus 16 Figures (available on request from the first author), IUCAA-28 To appear in The Astrophysical Journal, July 199