Friedmann Equations of FRW Universe in Scalar-tensor Gravity, f(R) Gravity and First Law of Thermodynamics

TL;DR

This paper extends the thermodynamic derivation of Friedmann equations to scalar-tensor and f(R) gravity theories, showing how horizon thermodynamics can describe universe dynamics beyond Einstein gravity.

Contribution

It introduces a method to derive Friedmann equations from thermodynamics in scalar-tensor and f(R) gravity, generalizing previous approaches.

Findings

Friedmann equations can be derived from horizon thermodynamics in scalar-tensor gravity.

Friedmann equations can be derived from horizon thermodynamics in f(R) gravity.

Implications for understanding gravity and cosmology beyond Einstein's theory.

Abstract

In the paper, hep-th/0501055 (R.G. Cai and S.P. Kim, JHEP {\bf 0502}, 050 (2005)), it is shown that by applying the first law of thermodynamics to the apparent horizon of an FRW universe and assuming the geometric entropy given by a quarter of the apparent horizon area, one can derive the Friedmann equations describing the dynamics of the universe with any spatial curvature; using the entropy formula for the static spherically symmetric black holes in Gauss-Bonnet gravity and in more general Lovelock gravity, where the entropy is not proportional to the horizon area, one can also obtain the corresponding Friedmann equations in each gravity. In this note we extend the study of hep-th/0501055 to the cases of scalar-tensor gravity and $f(R)$ gravity, and discuss the implication of results.