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

Journal Article · Sun Apr 15 04:00:00 EDT 2007 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.75.084003· OSTI ID:21020372

Akbar, M; Ronggen, Cai ^[1]

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1. Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735, Beijing 100080 (China)

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.

• OSTI ID: 21020372
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 8 Vol. 75; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BLACK HOLES
COSMOLOGY
ENERGY DENSITY
ENTROPY
FIELD EQUATIONS
GENERAL RELATIVITY THEORY
GRAVITATION
NONLUMINOUS MATTER
THERMODYNAMICS
UNIVERSE