Entropic-force dark energy reconsidered
  We reconsider the entropic-force model in which both kind of Hubble terms ${\dot H}$ and $H^{2}$ appear in the effective dark energy (DE) density affecting the evolution of the main cosmological functions, namely the scale factor, deceleration parameter, matter density and growth of linear matter perturbations. However, we find that the entropic-force model is not viable at the background and perturbation levels due to the fact that the entropic formulation does not add a constant term in the Friedmann equations. On the other hand, if on mere phenomenological grounds we replace the ${\dot H}$ dependence of the effective DE density with a linear term $H$ without including a constant additive term, we find that the transition from deceleration to acceleration becomes possible but the recent structure formation data strongly disfavors this cosmological scenario. Finally, we briefly compare the entropic-force models with some related DE models (based on dynamical vacuum energy) which overcome these difficulties and are compatible with the present observations. 
Spyros Basilakos and Joan Sola
astro-ph.CO gr-qc hep-ph hep-th