To further understand the relation between spacetime dynamics and horizon thermodynamics, in the Friedmann-Robertson-Walker spacetime, applying the first law of thermodynamics to apparent horizon of FRW spacetime, we derive the Friedmann equations describing dynamical evolution of the FRW universe, not only in Einstein gravity, but also in more general Lovelock gravity. We further find that the Friedmann equation can be cast to a universal form like the first law of thermodynamics, dE=TdS+WdV.  Applying this formulism, we find the universal form also holds in brane world scenarios and get entropy expressions associated with apparent horizon, establishing the relation between entropy expression and horizon geometry in brane world scenarios. More recently, we showed that there is indeed a Hawking radiation with temperature 1/2πr_A, for the apparent horizon of FRW spacetime, like black hole horizon; here r_A is the radius of the apparent horizon. This generalized Hawking’s study on Hawking radiation of black hole to the case of dynamical horizon in FRW universe.

These studies open a new direction to discuss the essential relation between dynamics of spacetime and horizon thermodynamics. It is quite helpful to further understand the holographic properties of gravity, Hawking radiation of black hole, thermodynamics of black hole and cosmological constant problem etc.  

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