论文标题
Cartan $ f（r）$重力和等效标量理论
Cartan $F(R)$ Gravity and Equivalent Scalar-Tensor Theory
论文作者
论文摘要
我们调查了$ f（r）$重力中的彩色形式主义。 $ f（r）$重力是作为一种理论引入的，可以通过替换$ r $ $ $ $的Einstein-Hilbert Action中的RICCI标量$ r $来解释宇宙学加速扩张。众所周知，$ f（r）$重力通过使用保形转换重写为标量张量理论。 Cartan $ F（R）$重力是根据Vierbein制定的Riemann-Cartan几何形状来描述的。在彩色形式主义中，RICCI标量$ r $分为两个部分，一个部分源自Levi-Civita连接，另一个源自扭转。假设旋转连接独立物质动作，我们已经成功地将Cartan $ f（r）$重力的动作重写为爱因斯坦 - 希尔伯特的动作，并具有具有规范动力学和潜在术语的标量场，而没有任何共同变换。由此产生的标量调整理论可用于应用通常的慢速场景。作为一个简单的情况，我们采用了Starobinsky模型，并评估宇宙学微波背景辐射中的波动。
We investigate the Cartan formalism in $F(R)$ gravity. $F(R)$ gravity has been introduced as a theory to explain cosmological accelerated expansion by replacing the Ricci scalar $R$ in the Einstein-Hilbert action with a function of $R$. As is well-known, $F(R)$ gravity is rewritten as a scalar-tensor theory by using the conformal transformation. Cartan $F(R)$ gravity is described based on the Riemann-Cartan geometry formulated by the vierbein. In the Cartan formalism, the Ricci scalar $R$ is divided into two parts, one derived from the Levi-Civita connection and the other from the torsion. Assuming the spin connection independent matter action, we have successfully rewritten the action of Cartan $F(R)$ gravity into the Einstein-Hilbert action and a scalar field with canonical kinetic and potential terms without any conformal transformations. The resulting scalar-tensor theory is useful in applying the usual slow-roll scenario. As a simple case, we employ the Starobinsky model and evaluate fluctuations in the cosmological microwave background radiation.
