TY - JOUR

T1 - Equilibrium thermodynamics in modified gravitational theories

AU - Bamba, Kazuharu

AU - Geng, Chao Qiang

AU - Tsujikawa, Shinji

N1 - Funding Information:
K.B. acknowledges the KEK theory exchange program for physicists in Taiwan and the very kind hospitality at KEK and Tokyo University of Science. S.T. thanks for the warm hospitality at National Tsing Hua University where the present work was initiated. The work by K.B. and C.Q.G. is supported in part by the National Science Council of R.O.C. under: Grant #s: NSC-95-2112-M-007-059-MY3 and NSC-98-2112-M-007-008-MY3 and National Tsing Hua University under the Boost Program and Grant #: 97N2309F1 . S.T. thanks financial support for the Grant-in-Aid for Scientific Research Fund of the JSPS (No. 30318802 ) and the Grant-in-Aid for Scientific Research on Innovative Areas (No. 21111006 ).

PY - 2010/4/26

Y1 - 2010/4/26

N2 - We show that it is possible to obtain a picture of equilibrium thermodynamics on the apparent horizon in the expanding cosmological background for a wide class of modified gravity theories with the Lagrangian density f (R, φ{symbol}, X), where R is the Ricci scalar and X is the kinetic energy of a scalar field φ{symbol}. This comes from a suitable definition of an energy-momentum tensor of the "dark" component that respects to a local energy conservation in the Jordan frame. In this framework the horizon entropy S corresponding to equilibrium thermodynamics is equal to a quarter of the horizon area A in units of gravitational constant G, as in Einstein gravity. For a flat cosmological background with a decreasing Hubble parameter, S globally increases with time, as it happens for viable f (R) inflation and dark energy models. We also show that the equilibrium description in terms of the horizon entropy S is convenient because it takes into account the contribution of both the horizon entropy over(S, ̂) in non-equilibrium thermodynamics and an entropy production term.

AB - We show that it is possible to obtain a picture of equilibrium thermodynamics on the apparent horizon in the expanding cosmological background for a wide class of modified gravity theories with the Lagrangian density f (R, φ{symbol}, X), where R is the Ricci scalar and X is the kinetic energy of a scalar field φ{symbol}. This comes from a suitable definition of an energy-momentum tensor of the "dark" component that respects to a local energy conservation in the Jordan frame. In this framework the horizon entropy S corresponding to equilibrium thermodynamics is equal to a quarter of the horizon area A in units of gravitational constant G, as in Einstein gravity. For a flat cosmological background with a decreasing Hubble parameter, S globally increases with time, as it happens for viable f (R) inflation and dark energy models. We also show that the equilibrium description in terms of the horizon entropy S is convenient because it takes into account the contribution of both the horizon entropy over(S, ̂) in non-equilibrium thermodynamics and an entropy production term.

KW - Cosmology

KW - Dark energy

KW - Evaporation

KW - Modified theories of gravity

KW - Quantum aspects of black holes

KW - Thermodynamics

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U2 - 10.1016/j.physletb.2010.03.070

DO - 10.1016/j.physletb.2010.03.070

M3 - Article

AN - SCOPUS:77950858021

SN - 0370-2693

VL - 688

SP - 101

EP - 109

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

IS - 1

ER -