Future evolution of bound superclusters in an accelerating Universe

The evolution of marginally bound supercluster-like objects in all accelerating Lambda cold dark matter (Lambda CDM) Universe is followed, by means of cosmological simulations, from the present time to all expansion factor a = 100. The objects are identified on the basis of the binding density criterion introduced by Dunner et al. Superclusters are identified with the ones whose mass M > 10(15) h(-1) M-circle dot, the most massive one with M similar to 8 x 10(15) h(-1) M-circle dot, comparable to the Shapley supercluster. The spatial distribution of the superclusters remains essentially the same after the present epoch, reflecting the halting growth of the cosmic web as Lambda gets to dominate the expansion of the Universe. The same trend can be seen ill the stagnation of the development of the mass function of virialized haloes and bound objects. The situation is considerably different when looking at the internal evolution, quantified in terms of their shape, compactness and density profile, and substructure in terms of their multiplicity function. We find a continuing evolution from a wide range of triaxial shapes at a = 1 to almost perfect spherical shapes at a = 100. We also find a systematic trend towards a higher concentration. Meanwhile, we see their substructure gradually disappearing, as the surrounding subclumps fall in and merge to form one coherent, virialized system.