Cosmic structure sizes in generic dark energy models

The maximum allowable size of a spherical cosmic structure as a function of its mass is determined by the maximum turn around radius R-TA,R-max, the distance from its center where the attraction on a radial test particle due to the spherical mass is balanced with the repulsion due to the ambient dark energy. In this work, we extend the existing results in several directions. (a) We first show that, for w not equal -1, the expression for RTA, max found earlier, using the cosmological perturbation theory, can be derived using a static geometry as well. (b) In the generic dark energy model with arbitrary time dependent state parameter w(t), taking into account the effect of inhomogeneities upon the dark energy as well, it is shown that the data constrain w(t = today) > -2.3. (c) We address the quintessence and the generalized Chaplygin gas models, both of which are shown to predict structure sizes consistent with observations.