论文标题
一般相对论和$ f（r）$修饰的重力，爱因斯坦和约旦框架的宇宙常数
Study of General Relativity and $f(R)$ Modified Gravity with Cosmological Constant for Einstein and Jordan Frames
论文作者
论文摘要
该论文研究了公制形式主义中一类改良的重力理论中通货膨胀的玩具模型。而不是标准过程 - 假设约旦框架中的非线性拉格朗日$ f（r）$，我们从爱因斯坦框架中的简单ϕ^2开始，并研究了前图中的相应的$ f（r）$。 Such approach yields plenty of new pieces of information, namely a self-terminating inflationary solution with a linear Lagrangian, a robust criterion for stability of such theories, a dynamical effective potential for the Ricci scalar $R$, 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.
This thesis investigates 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 ϕ^2 potential in the Einstein frame and investigate the corresponding $f(R)$ in the former picture. Such approach yields plenty of new pieces of information, namely a self-terminating inflationary solution with a linear Lagrangian, a robust criterion for stability of such theories, a dynamical effective potential for the Ricci scalar $R$, 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.
