Uncertainty Relation And Thermodynamics Of The Apparent Horizon Of FRW Universe

An investigation into the relation between the uncertainty relation and thermodynamics of the apparent horizon of Friedmann-Robertson-Walker (FRW) universe is given.Regarding this aspect,Rong-Gen Cai et al.has derived the equation of dynamics of the universe(Friedmann Equation) by applying the first law of thermodynamics to the apparent horizon of FRW universe.Based on Cai's work and the uncertainty relation,we study the important parameters in the thermodynamics of the apparent horizon of FRW universe—the temperature and entropy on the apparent horizon.Firstly,we give an introduction to the derivation of Friedmann equation by making use of Einstein equation and FRW metric.Secondly,we review the method given by Cai et al.about how to derive Friedmann equation by applying the first law of thermodynamics to the apparent horizon of FRW universe.Finally,it is shown that the temperature and entropy on the apparent horizon of FRW universe get corrections if one considers the effect of the generalized uncertainty principle(GUP),the extended uncertainty principle (EUP) or the generalized extended uncertainty principle(GEUP).Then,we make our conclusions:firstly,the temperature on the apparent horizon gets a positive correction and increases;secondly,the entropy on the apparent horizon gets a negative correction and decreases;thirdly,the GUP gives the entropy on the apparent horizon a negative logarithmic correction term, which conforms to the negative logarithmic correction to the Bekenstein-Hawking entropy of black holes from loop quantum gravity.