Cosmological mass function with 1D gravity - art. no. 103502

The cosmological mass function problem is analyzed in full detail in the ca se of 1D gravity, with analytical, semianalytical, and numerical techniques . The extended Press and Schechter theory is improved by detailing the rela tion between smoothing radius and mass of the objects. This is done by intr oducing in the formalism the concept of a growth curve for the objects. The predictions of the extended Press and Schechter theory are compared to lar ge N-body simulations of flat expanding 1D universes with scale-free power spectra of primordial perturbations. The collapsed objects in the simulatio ns are located with a clump-finding algorithm designed to find regions that have undergone orbit crossing or that are in the multistream regime (these are different as an effect of the finite size of the multistream regions). It is found that the semianalytical mass function theory. which has no fre e parameters, is able to recover the properties of collapsed objects both s tatistically and object by object. in particular, the predictions of region s in orbit crossing are optimized by the use of Gaussian filtering, while t he use of sharp k-space filtering apparently allows to reproduce the larger multistream regions. The mass function theory does not reproduce well the clumps found with the standard friends-of-friends algorithm; however, the p erformance of this algorithm has not been thoroughly tested in the 1D cosmo logy. Our preliminary analyses of the 3D case confirms that the techniques developed in this paper are precious in understanding the cosmological mass function problem in 3D. [S0556-2821(99)09618-6].