Thermodynamics of the FRW universe in rainbow gravity

Rainbow gravity can be a suitable model to study the Friedmann–Robertson–Walker (FRW) universe in the realm of high energy physics. In rainbow gravity the radius of the apparent horizon is modified and it is used to derive the surface gravity and the temperature on the horizon. Inspired by the modified Friedmann equation in rainbow gravity and adopting the viewpoint that there is a deep connection between Friedmann equation and the first law of thermodynamics, the entropy on the horizon is obtained. It is interesting to be noted that the thermodynamical properties of the FRW universe depend on the energy of the probe, which is used by an observer to investigate the spacetime. Finally, it is shown that the validity of the generalized second law (GSL) of thermodynamics can be considered as a useful instrument to restrict the choice of rainbow gravity functions.