论文标题
渐进式渐进公式
Interpolation formulas for asymptotically safe cosmology
论文作者
论文摘要
提出了简单的插值公式，以描述重新归一化组（RG）在2参数框架Einstein-Hilbert（EH）重力理论中的重力耦合量表依赖性，并应用于简单的，可实现的，可实现的，可实现的，空间上均匀的，同质的和同质的，以及同性恋，同性恋，同性恋平面模型。在两个方案中发现了分析解决方案，其中包含了RG级$ K $的转换规则$ K（t）$ k $ to cosmological Time $ t $的不同方法。在讨论的模型的情况下，这些方案结果证明了相同的宇宙学演化。对于转换规则$ k（t）$以及特征性时间尺度$ t_g $和$t_λ> t_g $的特征时间尺度发现了明确的分析公式，分别对应于动态能量尺度$ k_g $和$k_λ$，引起了EH理论的RG分析。结果表明，存在一个与模型有关的时间尺度$ t_d $（$ t_g \ le t_d <t_λ$），其中加速扩展会变化对减速的变化。结果表明，进化从识别良好的宇宙学固定点到另一个。作为副产品，我们表明，由于量子效应，系统的熵在间隔$ 0 <t \ let_λ$中单调减少。
Simple interpolation formulas are proposed for the description of the renormalization group (RG) scale dependences of the gravitational couplings in the framework of the 2-parameters Einstein-Hilbert (EH) theory of gravity and applied to a simple, analytically solvable, spatially homogeneous and isotropic, spatially flat model universe. The analytical solution is found in two schemes incorporating different methods of the determination of the conversion rule $k(t)$ of the RG scale $k$ to the cosmological time $t$. In the case of the discussed model these schemes turn out to yield identical cosmological evolution. Explicit analytical formulas are found for the conversion rule $k(t)$ as well as for the characteristic time scales $t_G$ and $t_Λ>t_G$ corresponding to the dynamical energy scales $k_G$ and $k_Λ$, respectively, arising form the RG analysis of the EH theory. It is shown that there exists a model-dependent time scale $t_d$ ($t_G\le t_d<t_Λ$) at which the accelerating expansion changes to the decelerating one. It is shown that the evolution runs from a well-identified cosmological fixed point to another one. As a by-product we show that the entropy of the system decreases monotonically in the interval $0<t\le t_Λ$ due to the quantum effects.
