Modified Friedmann Equations on the Brane from Entropic Force

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. Keywords Entropic force · Brane cosmology · GravityThe 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].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 ( )

Energy Definition and Dark Energy: A Thermodynamic Analysis

“…which clearly differs from (5) unless we have a pressureless fluid [41,47]. Although this energy definition has originally been obtained by using the Einstein field equations [47], it is in accordance with various thermodynamic and holographic approaches [34][35][36][37][38][39][40][41][42][43][44][45][46]. In fact, if we accept this energy definition as a basic equation and not a secondary equation [34][35][36][37], then there are various thermodynamic and holographic approaches employed to get the Friedmann and gravitational field equations in various theories by using the Komar mass definition [34][35][36][37][38][39][40][41][42][43][44][45][46].…”

From the Komar Mass and Entropic Force Scenarios to the Einstein Field Equations on the Ads Brane

“…By taking the entropic origin of the gravity into account, authors of [42] tried to find the Friedmann equations on the brane. In addition, author of [43] has considered corrected entropy of the horizon and found the modified Friedmann equations on the brane from the entropic force. In these approaches [42,43], authors have introduced a same definition for the Komar mass on the brane.…”

“…In addition, author of [43] has considered corrected entropy of the horizon and found the modified Friedmann equations on the brane from the entropic force. In these approaches [42,43], authors have introduced a same definition for the Komar mass on the brane. In this paper, based on the Komar definition for the mass in n-dimensions, we try to build the (n + 1)-dimensional Einstein field equations using the entropic force approach.…”

Entropic gravity from noncommutative black holes

“…In fact, this approach helps us to provide a thermodynamic description of the gravitational field equations in various theories . Since the entropy formula plays a key role in this approach, any modification of the system entropy may affect the gravitational field equations and therefore the corresponding Friedmann equations [16][17][18][19]. Moreover, it is worthwhile mentioning here that Verlinde's interpretation of the origin of gravity and space-time is in line with both the generalized entropy formula and its corresponding cosmology [36].…”