The influence of the generalized uncertainty principle (GUP) and extended uncertainty principle (EUP) on the thermodynamics of the Friedmann-Robertson-Walker (FRW) universe has been investigated. It is shown that the entropy of the apparent horizon of the FRW universe gets a correction if one considers the effect of the GUP or EUP. Moreover, starting with the modified entropy and applying the first law of thermodynamics, dE = T dS, to the apparent horizon of the FRW universe, we obtain the modified Friedmann equations. The influence of the GUP or EUP on the thermodynamics of the FRW universe provides a deep insight into the understanding of the quantum gravity or large length scale corrections to the dynamics of the FRW universe.

In this paper, we study the thermodynamic quantities of Friedmann-Robertson-Walker (FRW) universe by using the tunneling formalism beyond semiclassical approximation developed by Banerjee and Majhi [25]. For this we first calculate the corrected Hawking-like temperature on apparent horizon by considering both scalar particle and fermion tunneling. With this corrected Hawking-like temperature, the explicit expressions of the corrected entropy of apparent horizon for various gravity theories including Einstein gravity, Gauss-Bonnet gravity, Lovelock gravity, f (R) gravity and scalar-tensor gravity, are computed. Our results show that the corrected entropy formula for different gravity theories can be written into a general expression (4.39) of a same form. It is also shown that this expression is also valid for black holes. This might imply that the expression for the corrected entropy derived from tunneling method is independent of gravity theory, spacetime and dimension of the spacetime. Moreover, it is concluded that the basic thermodynamical property that the corrected entropy on apparent horizon is a state function is satisfied by the FRW universe.

We extend the recently proposed Kerr/CFT correspondence to examine the dual conformal field theory of four dimensional Kaluza-Klein black hole in Einstein-Maxwell-Dilaton theory. For the extremal Kaluza-Klein black hole, the central charge and temperature of the dual conformal field are calculated following the approach of Guica, Hartman, Song and Strominger. Meanwhile, we show that the microscopic entropy given by the Cardy formula agrees with Bekenstein-Hawking entropy of extremal Kaluza-Klein black hole. For the non-extremal case, by studying the near-region wave equation of a neutral massless scalar field, we investigate the hidden conformal symmetry of Kaluza-Klein black hole, and find the left and right temperatures of the dual conformal field theory.Furthermore, we find that the entropy of non-extremal Kaluza-Klein black hole is reproduced by Cardy formula.