Thermodynamic behavior of the Friedmann equation at the apparent horizon of the FRW universe

By M. Akbar, R. Cai. 2006

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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 r-tilde{sub 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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/f363bba28fc554c19cdb05f3901e69cd06bc08c7

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In Astronomy and Astrophysics

In Nuclear and High Energy Physics

Citations in the corpus

f(R) Theories (2010, methodology): “Even in the FLRW spacetime, however, the Friedmann equation can be written in the thermodynamical form TdS = −dE +WdV , where W is the work density present in the dynamical background [8].”