Abstract
The well-known area relation of the black hole entropy can be modified from the inclusion of quantum effects, motivated from the loop quantum gravity. Applying this modified entropy-area relation to brane cosmology, we derive the modified cosmological equations governing the evolution of the universe on the brane. We adopt the viewpoint that interprets gravity as an entropic force caused by the changes in the information when a material body moves away from the holographic screen.
Abstract
The profound connection between black hole physics and thermodynamics, throws new light to the genius of gravity. This fact leads some physicists investigating gravity from the point of view of thermodynamics. Jacobson [1] was the first who derived Einstein's gravitational field equation from the first law of thermodynamics. This derivation suggests that Einstein equation for the spacetime metric has a predisposition to thermodynamic behavior. The study on the connection between thermodynamics and gravity has been generalized to the cosmological situations [2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The further investigations of Padmanabhan [16] reinterpreted entropy as the equipartition rule of energy. It also provided a thermodynamic interpretation of gravity. These results support that the gravity has an entropic origin [17][18][19].
Abstract
A constructive new idea on the relation between gravity and thermodynamics was recently proposed by Verlinde [20] who claimed that gravity is not a fundamental interaction and can be interpreted as an entropic force arising from the change of information when a material body moves away from the holographic screen. Among various interesting observations made by Verlinde, here we mention two of them. First, with the assumption of the A. Sheykhi ( ) 

entropic force together with the Unruh temperature, Verlinde is able to derive the second law of Newton. Second, taking into account the entropic force together with the holographic principle and the equipartition law of energy leads to Newton's law of gravitation. Similar discoveries were also made by Padmanabhan [16] . He observed that, using the equipartition law of energy for the horizon degrees of freedom together with the thermodynamic relation S = E/2T , one can obtain Newton's law of gravity. Here S and T are thermodynamic entropy and the temperature associated with the horizon, and E is the active gravitational mass which produces the gravitational acceleration in the spacetime [21] .

Let us begin with reviewing the Verlinde's argument. Motivated by Bekenstein's entropy bound, Verlinde postulated that when a test particle with mass m approaches a holographic screen from a distance x, the change of entropy on the holographic screen is

According to Verlide's argument when a particle has an entropic reason to be on one side of the screen and the screen carries a temperature, it will experience an entropic force equal to

Thus, in order to have a non zero force, we need to have a non vanishing temperature. Here x is the displacement of the particle from the holographic screen, while T and S are the temperature and the entropy change on the screen, respectively. Inserting (1) into (2) the entropic force is simplified as

Assuming the holographic screen forms a closed surface. More specifically, let us assume it is a sphere with radius R. The key statement is that we need to have a temperature in order to have a force. One can think about the boundary as a storage device for information. Assuming that the holographic principle holds, the maximal storage space, or total number of bits, is proportional to the area A. Let us denote the number of used bits by N . It is natural to assume that this number will be proportional to the area A. Thus we write

where the constant of proportionality is chosen for later convenience. Suppose there is a total energy E present in the system. According to the holographic principle the energy is divided evenly over the bits N on the screen. Then, according to the equipartition law of energy [16] the total energy on the surface is

We also identify the energy of the holographic surface S with the relativistic mass

where M represents the mass that would emerge in the part of space enclosed by the screen. Finally, combining (3)-(6), and using relation A = 4πR 2 , one immediately finds the Newton's law of gravitation

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