It is shown that the differential form of Friedmann equation of a FRW universe can be rewritten as the first law of thermodynamics $dE=TdS+WdV$ at apparent horizon, where $E=\rho V$ is the total energy of matter inside the apparent horizon, $V$ is the volume inside the apparent horizon, $W=(\rho -P)/2$ is the work density, $\rho$ and $P$ are energy density and pressure of matter in the universe, respectively. From the thermodynamic identity one can derive that the apparent horizon ${\tilde{r}}_A$ has associated entropy $S=A/4G$ and temperature $T=\kappa /2\pi$ in Einstein general relativity, where $A$ is the area of apparent horizon and $\kappa$ is the surface gravity at apparent horizon of FRW universe. We extend our procedure to the Gauss-Bonnet gravity and more general Lovelock gravity and show that the differential form of Friedmann equations in these gravities can also be written as $dE=TdS+WdV$ at the apparent horizon of FRW universe with entropy $S$ being given by expression previously known via black hole thermodynamics.

• Received 5 January 2007

DOI:https://doi.org/10.1103/PhysRevD.75.084003