THE EVOLUTION OF VOIDS IN THE ADHESION APPROXIMATION

We apply the adhesion approximation to study the formation and evoluti on 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 sp ectrum evolves with time and that the mean void size in the standard C OBE-normalized cold dark matter (CDM) model with h50 = 1 scales approx imately as D(z)BAR = D0BAR/(1 + z)1/2, where D0BAR congruent-to 10.5 M pc. Interestingly, we find a strong correlation between the sizes of v oids and the value of the primordial gravitational potential at void c enters. This observation could in principle, pave the way toward recon structing the form of the primordial potential from a knowledge of the observed void spectrum. Studying the void spectrum at different cosmo logical epochs, for spectra with a built in k-space cutoff we find tha t the number of voids in a representative volume evolves with time. Th e mean number of voids first increases until a maximum value is reache d (indicating that the formation of cellular structure is complete), a nd then begins to decrease as clumps and filaments merge leading to hi erarchical clustering and the subsequent elimination of small voids. T he cosmological epoch characterizing the completion of cellular struct ure occurs when the length scale going nonlinear approaches the mean d istance between peaks of the gravitational potential. A central result of this paper is that voids can be populated by substructure such as mini-sheets and filaments, which run through voids. The number of such mini-pancakes that pass through a given void can be measured by the g enus characteristic of an individual void which is an indicator of the topology of a given void in initial (Lagrangian) space. Large voids h ave on an average a larger measure than smaller voids indicating more substructure within larger voids relative to smaller ones. We find tha t the topology of individual voids is strongly epoch dependent, with v oid topologies generally simplifying with time. This means that as voi ds grow older they become progressively more empty and have less subst ructure within them. We evaluate the genus measure both for individual voids as well as for the entire ensemble of voids predicted by CDM mo del. As a result we find that the topology of voids when taken togethe r with the void spectrum is a very useful statistical indicator of the evolution of the structure of the universe on large scales.