Equilibrium thermodynamics in modified gravitational theories

Kazuharu Bamba*, Chao Qiang Geng, Shinji Tsujikawa

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

68 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)101-109
Number of pages9
JournalPhysics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Issue number1
Publication statusPublished - 2010 Apr 26
Externally publishedYes


  • Cosmology
  • Dark energy
  • Evaporation
  • Modified theories of gravity
  • Quantum aspects of black holes
  • Thermodynamics

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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