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 $R_{\rm TA,max}$, the distance from its centre 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 $w\neq -1$, the expression for $R_{\rm TA, max}$ 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, where it is shown that the data constrain $w(t={\rm today})>-2.3$, and (c) in the quintessence and the generalized Chaplygin gas models, both of which are shown to predict structure sizes consistent with observations.Comment: v2, 19pp; added references and discussions, improved presentation; accepted in EPJ

Comments on the entropic gravity proposal

Explicit tests are presented of the conjectured entropic origin of the gravitational force. The gravitational force on a test particle in the vicinity of the horizon of a large Schwarzschild black hole in arbitrary spacetime dimensions is obtained as entropic force. The same conclusion can be reached for the cases of a large electrically charged black hole and a large slowly rotating Kerr black hole. The generalization along the same lines to a test mass in the field of an arbitrary spherical star is also studied and found not to be possible. Our results thus reinforce the argument that the entropic gravity proposal cannot account for the gravitational force in generic situations.Comment: v2, 20pp, 1fig; added references and discussions; improved presentation; accepted in EPJ