论文标题
重力的有效场方程和依赖比例的耦合
Effective field equations and scale-dependent couplings in gravity
论文作者
论文摘要
在物质存在下，牛顿的常数$ g（x）$和宇宙常数$λ（x）$的一组新的字段方程式出现。我们证明，它代表了数学上最一致的一致，物理上合理的，一组演化方程，假设动态变量中最多是第二个衍生物。在新的爱因斯坦方程中，仅出现$λ$ - 运动术语，而在修改后的保护方程中，也出现了$ g $的衍生术语。作为一种应用，这种形式主义是在早期宇宙的渐近安全场景的背景下应用的，假设具有状态辐射方程的完美液体。对于所有类型的空间曲率，获得了宇宙学解决方案，并显示了各种有趣的宇宙发展。为了表明此类行为，详细讨论了具有瞬态加速时代的弹跳解决方案，回忆解决方案或非单明的扩展解决方案。
A new set of field equations for a space-time dependent Newton's constant $G(x)$ and cosmological constant $Λ(x)$ in the presence of matter is presented. We prove that it represents the most general mathematically consistent, physically plausible, set of evolution equations assuming at most second derivatives in the dynamical variables. In the new Einstein's equations, only $Λ$-kinetic terms arise, while in the modified conservation equation, derivative terms of $G$ also appear. As an application, this formalism is applied in the context of the Asymptotic Safety scenario to the early universe, assuming a perfect fluid with a radiation equation of state. Cosmological solutions are obtained for all types of spatial curvature, displaying a variety of interesting cosmic evolutions. As an indication of such behaviours, bouncing solutions, recollapsing solutions or non-singular expanding solutions with a transient acceleration era are discussed in details.
