Modified Friedmann equations from Debye entropic gravity

Abstract

A remarkable new idea on the origin of gravity was recently proposed by Verlinde who claimed that the laws of gravitation are no longer fundamental, but rather emerge naturally as an entropic force. In Verlinde derivation, the equipartition law of energy on the holographic screen plays a crucial role. However, the equipartition law of energy fails at the very low temperature. Therefore, the formalism of the entropic force should be modified while the temperature of the holographic screen is very low. Considering the Debye entropic gravity and following the strategy of Verlinde, we derive the modified Newton's law of gravitation and the corresponding Friedmann equations which are valid in all range of temperature. In the limit of strong gravitational field, i.e. high temperature compared to Debye temperature, T ≫ TD, one recovers the standard Newton's law and Friedmann equations. We also generalize our study to the entropy corrected area law and derive the dynamical cosmological equations for all range of temperature. Some limits of the obtained results are also studied.

Entropic corrections to Friedmann equations in the extra dimensional FRW universe

“…They have the same form as those obtained in literatures which have been obtained from other alternative approaches. [41][42][43]45,46 Also, the results have the same structure as those obtained from purturbative quantum gravity.…”

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].…”

“…In the above equations, p is the pressure of the fluid. By combining (18) and ( 20) we obtain the acceleration equation as being…”

Thermodynamical description of the ghost dark energy model

“…28 This hypothesis is generalized to various theories of gravity and cosmological setups. [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43] Therefore, the tendency of the cosmos, as a closed system, to increase its entropy is compatible with the current accelerated phase of the expansion. Finally, we should note that the thermodynamic analysis of the universe helps us to get a better understanding from the gravity, the universe, its origin and evolution, and thus the nature of the mysterious dominated fluid supporting the current accelerated expansion.…”

“…In fact, the tendency of the universe to rise its entropy can be interpret as an origin for the gravity and thus the Einstein equations [28]. This hypothesis is generalized to various theories of gravity and cosmological setups [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]. Therefore, the tendency of the cosmos, as a closed system, to increase its entropy is compatible with the current accelerated phase of the expansion.…”