This paper starts from a toy model for inflation in a class of modified theories of gravity in the metric formalism. Instead of the standard procedure -- assuming a non-linear Lagrangian $f(R)$ in the Jordan frame -- we start from a simple $\phi^2$ potential in the Einstein frame and investigate the corresponding $f(R)$ in the former picture. The addition of an ad-hoc Cosmological Constant in the Einstein frame leads to a Thermodynamical interpretation of this physical system, which allows further insight on its (meta)stability and evolution.

中文翻译：

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f(R) 引力理论的热力学

本文从度量形式主义中一类修正的引力理论中的通货膨胀玩具模型开始。代替标准程序——假设 Jordan 框架中的非线性拉格朗日 $f(R)$——我们从爱因斯坦框架中的一个简单的 $\phi^2$ 势开始，并研究相应的 $f(R) $ 在前一张图片中。在爱因斯坦坐标系中添加一个特别的宇宙常数导致对该物理系统的热力学解释，从而可以进一步了解其（亚）稳定性和演化。