Entropic force and its cosmological implications
We investigate a possibility of realizing the entropic force into the cosmology. A main issue is how the holographic screen is implemented in the Newtonian cosmology. Contrary to the relativistic realization of Friedmann equations, we do not clarify the connection between Newtonian cosmology and entropic force because there is no way of implementing the holographic screen in the Newtonian cosmology.http://arxiv.org/abs/1005.2240
However, one of urgent issues to resolve is to answer to the question of how one can construct a spherical holographic screen of radius R which encloses a source mass M located at the origin to understand the entropic force. This is a critical and important issue because the holographic screen (an exotic description of spacetime) originates from relativistic approaches to black hole [32, 33] and cosmology [34]. Verlinde has introduced this screen by analogy with an absorbing process of a particle around the event horizon of black hole. Considering a smaller test mass m located at ∆x away from the screen 2 and getting the change of entropy on the screen, its behavior should resemble that of a particle approaching a stretched horizon of a black hole, as described by Bekenstein [2]. Before proceeding, we would like to mention what is the difference between Newtonian gravity and general relativity [35]. First Newtonian gravity is an action-at-a-distance, that is, the gravitational influence propagates instantaneously (c → ∞), implying the violation of causality. Second, Newtonian gravity is ignorant of the presence of horizon where the relativistic effects are supposed to dominates. For example, the horizons are considered as either the event horizon of black hole or the apparent horizons in the Friedmann- Robertson-Walker (FRW) universe. Comparing Newtonian gravity and general relativity in cosmology is different than in the case of isolated, asymptotically flat systems [36]. For isolated systems, both Newtonian gravity and general relativity are well-defined. In con- trast, while relativistic cosmology is well-defined, there is no unique way to accommodate Newtonian theory of cosmology because the Newtonian equations are only defined up to boundary terms which have to be specified at all times. Hence it is not easy to implement the entropic force into the cosmological setting. In the literatures [7, 9, 11], the authors did not mention explicitly how the entropic force (3) works for the cosmological purpose. It seems that the entropic force is not realized in the Newtonian cosmology unless the holographic screen is clearly defined.
