arXiv 2201.058272022-01gr-qcastro-ph.COhep-phhep-th

宇宙时空中真空能的重整化：对宇宙学常数问题的启示

Renormalizing the vacuum energy in cosmological spacetime: implications for the cosmological constant problem

Cristian Moreno-Pulido, Joan Sola Peracaula

备注：: Typos corrected, references added
发表信息：: Eur. Phys. J. C82, 551 (2022)
DOI：: 10.1140/epjc/s10052-022-10484-w

摘要：

量子场论中真空能量的重整化通常受到理论难题的困扰，不仅与重整化过程本身有关，而且与最终结果通常导致与宇宙学中$Λ$的测量值不相容的非常大（有限）的贡献这一事实有关。在这里，我们计算零点能量（ZPE）的非最小耦合（大质量）的标量场在FLRW时空中使用的离壳绝热重整化技术在以前的工作。一般的离壳结果产生了一个光滑函数$ρ_{\rm vac}(H)$，它由哈勃速率的幂和/或它的时间导数组成，涉及不同的（偶数）绝热阶数$\sim H^N$（$N=0,2,4,6,...)$），也就是说，它非常明显地导致了运行真空模型（RVM）的结构。我们已经从有效作用量形式主义中验证了同样的结果，并用它来寻找运行量子真空的$β$函数。没有出现来自粒子质量的不期望的贡献$\sim m^4$，因此在$ρ_{\rm vac}(H)$中不需要对参数进行微调。此外，我们还发现更高功率的$\sim H^6$可以自然地驱动早期宇宙中的RVM暴胀。我们的计算还详细阐明了量子真空的状态方程：它被证明不是严格的PDMATHAMT，而是适度的动力学。低能量下的$ρ_{\rm vac}(H)$形式也是RVM的特征，它由一个加性项（所谓的“宇宙学常数”）和一个小的动力学分量$\sim νH^2$（$|ν|\ll1$）组成。最后，我们预测了牛顿引力耦合$G(H)$的慢（$\sim\ln H$）运行。我们的半经典QFT计算的物理结果是揭示：今天的宇宙真空和引力强度都应该是温和的动力学。

英文摘要：

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.

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