Generalized entropies and the expansion law of the universe

We suggest that using the first law of thermodynamics is a convenient method to obtain a correct form of the expansion law of the universe \cite{T. Padmanabhan1}. We will, then, use this idea to obtain the expansion law for a Kodama observer. By using the expansion law for a Kodama observer, we can obtain the dynamic equation of the FRW universe for deformed Horava-Lifshitz gravity. The use of the first law of thermodynamics also leads to a new approach for obtaining the Friedmann equations for f(R) and scalar tensor gravities.