Friedmann Equation

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M Akbar - One of the best experts on this subject based on the ideXlab platform.

  • thermodynamic behavior of the Friedmann Equation at the apparent horizon of the frw universe
    Physical Review D, 2007
    Co-Authors: M Akbar
    Abstract:

    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.

  • thermodynamic behavior of the Friedmann Equation at the apparent horizon of the frw universe
    Physical Review D, 2007
    Co-Authors: M Akbar, Ronggen Cai
    Abstract:

    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 $E=\ensuremath{\rho}V$ is the total energy of matter inside the apparent horizon, $V$ is the volume inside the apparent horizon, $W=(\ensuremath{\rho}\ensuremath{-}P)/2$ is the work density, $\ensuremath{\rho}$ and $P$ are energy density and pressure of matter in the universe, respectively. From the thermodynamic identity one can derive that the apparent horizon ${\stackrel{\texttildelow{}}{r}}_{A}$ has associated entropy $S=A/4G$ and temperature $T=\ensuremath{\kappa}/2\ensuremath{\pi}$ in Einstein general relativity, where $A$ is the area of apparent horizon and $\ensuremath{\kappa}$ 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.

Steven Willison - One of the best experts on this subject based on the ideXlab platform.

Tuomas Multamaki - One of the best experts on this subject based on the ideXlab platform.

Yongqiang Wang - One of the best experts on this subject based on the ideXlab platform.

Aurelien Barrau - One of the best experts on this subject based on the ideXlab platform.