Redshift-space limits of bound structures

An exponentially expanding Universe, possibly governed by a cosmological constant, forces gravitationally bound structures to become more and more isolated, eventually becoming causally disconnected from each other and forming so-called "island universes". This new scenario reformulates the question about which will be the largest structures that will remain gravitationally bound, together with requiring a systematic tool that can be used to recognize the limits and mass of these structures from observational data, namely redshift surveys of galaxies. Here we present a method, based on the spherical collapse model and N-body simulations, by which we can estimate the limits of bound structures as observed in redshift space. The method is based on a theoretical criterion presented in a previous paper that determines the mean density contrast that a spherical shell must have in order to be marginally bound to the massive structure within it. Understanding the kinematics of the system, we translated the real-space limiting conditions of this "critical" shell to redshift space, producing a projected velocity envelope that only depends on the density profile of the structure. From it we created a redshift-space version of the density contrast that we called "density estimator", which can be calibrated from N-body simulations for a reasonable projected velocity envelope template, and used to estimate the limits and mass of a structure only from its redshift-space coordinates.