Thermodynamics of $f(R)$ Gravity with Disformal Transformation

Abstract

We study thermodynamics in $f(R)$ gravity with the disformal transformation. The transformation applied to the matter Lagrangian has the form of $\g_{\m\n} = A(ϕ,X)g_{\m\n} + B(ϕ,X)\pa_\m\f\pa_\n\f$ with the assumption of the Minkowski matter metric $\g_{\m\n} = \e_{\m\n}$, where $\varphi$ is the disformal scalar and $X$ is the corresponding kinetic term of $\varphi$. We verify the generalized first and second laws of thermodynamics in this disformal type of $f(R)$ gravity in the Friedmann-Lemaître-Robertson-Walker (FLRW) universe. In addition, we show that the Hubble parameter contains the disformally induced terms, which define the effectively varying equations of state for matter.

arXiv comment23 pages, no figure, published version in Entropy 21, 172 (2019)

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• Thermodynamical correspondence of $f(R)$ gravity in Jordan and Einstein frames
• Thermodynamics and decay of de Sitter vacuum
• First law of thermodynamics and entropy of FLRW universe in modified gravity
• Emergence of space and expansion of universe
• Thermal stability of a special class of black hole solutions in F(R) gravity