Abstract
It is shown that the differential form of Friedmann equation of a FRW universe can be rewritten as the first law of thermodynamics at apparent horizon, where is the total energy of matter inside the apparent horizon, is the volume inside the apparent horizon, is the work density, and are energy density and pressure of matter in the universe, respectively. From the thermodynamic identity one can derive that the apparent horizon has associated entropy and temperature in Einstein general relativity, where is the area of apparent horizon and 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 at the apparent horizon of FRW universe with entropy being given by expression previously known via black hole thermodynamics.
- Received 5 January 2007
DOI:https://doi.org/10.1103/PhysRevD.75.084003
©2007 American Physical Society