论文标题
在宇宙时空重新归一化的真空能量：对宇宙恒定问题的影响
Renormalizing the vacuum energy in cosmological spacetime: implications for the cosmological constant problem
论文作者
论文摘要
量子场理论（QFT）中真空能的重新归一化通常与理论难题不仅与重新归一化过程本身相关，而且还与最终结果通常导致非常大的（有限的）贡献与宇宙中的$λ$相关的$λ$不相容。本文中，我们使用先前工作中使用的脱壳绝热的重新归一化技术来计算FLRW时空中非最小耦合（巨大的）标量场的零点能量（ZPE）。一般的外壳结果产生了平稳的函数$ρ_ {\ rm vac}（h）$，由哈勃速率和/或其时间派生剂的功率制成，涉及不同（偶数）绝热的订单$ \ sim h^n $（$ \ sim h^n $（$ n = 0,2,4,4,6，...）$。我们已经验证了有效的作用形式主义的相同结果，并用它来找到运行量子真空的$β$功能。没有出现粒子质量中的$ \ sim m^4 $ $ \ sim m^4 $，因此在$ρ_ {\ rm vac}（h）$中不需要对参数进行微调。此外，我们发现较高的功率$ \ sim h^6 $自然可以在早期的宇宙中驱动RVM通信。我们的计算还详细阐明了量子真空状态的方程：事实证明它不完全$ -1 $，并且是中等动力的。 $ρ_ {\ rm vac}（h）$在低能的形式也是RVM的特征，并由一个加法项（所谓的“宇宙常数”）以及一个小的动态组件$ \ sim门νH^2 $（$ | c | n | n | \ \ ll1 $）组成。最后，我们预测牛顿重力耦合$ g（h）$的缓慢（$ \ sim \ ln H $）。我们的半经典QFT计算的物理结果揭示了：当今的宇宙真空和重力强度都应该是温和的。
The renormalization of the vacuum energy in quantum field theory (QFT) is usually plagued with theoretical conundrums related not only with the renormalization procedure itself, but also with the fact that the final result leads usually to very large (finite) contributions incompatible with the measured value of $Λ$ in cosmology. Herein, we compute the zero-point energy (ZPE) for a nonminimally coupled (massive) scalar field in FLRW spacetime using the off-shell adiabatic renormalization technique employed in previous work. The general off-shell result yields a smooth function $ρ_{\rm vac}(H)$ made out of powers of the Hubble rate and/or of its time derivatives involving different (even) adiabatic orders $\sim H^N$ ($N=0,2,4,6,...)$, i.e. it leads, remarkably enough, to the running vacuum model (RVM) structure. We have verified the same result from the effective action formalism and used it to find the $β$-function of the running quantum vacuum. No undesired contributions $\sim m^4$ from particle masses appear and hence no fine-tuning of the parameters is needed in $ρ_{\rm vac}(H)$. Furthermore, we find that the higher power $\sim H^6$ could naturally drive RVM-inflation in the early universe. Our calculation also elucidates in detail the equation of state of the quantum vacuum: it proves to be not exactly $-1$ and is moderately dynamical. The form of $ρ_{\rm vac}(H)$ at low energies is also characteristic of the RVM and consists of an additive term (the so-called `cosmological constant') together with a small dynamical component $\sim νH^2$ ($|ν|\ll1$). Finally, we predict a slow ($\sim\ln H$) running of Newton's gravitational coupling $G(H)$. The physical outcome of our semiclassical QFT calculation is revealing: today's cosmic vacuum and the gravitational strength should be both mildly dynamical.
