arXiv 2110.080702021-10-15gr-qchep-ph

无$m^4$项的重整化$ρ_{\rm vac}$

Renormalized $ρ_{\rm vac}$ without $m^4$ terms

Cristian Moreno-Pulido, Joan Sola Peracaula

备注：: 19 pages, 0 figures. arXiv admin note: text overlap with arXiv:2005.03164

摘要：

爱因斯坦方程中的宇宙学常数项$Λ$，在过去的三十年里一直是宇宙学和谐或标准$Λ$ CDM模型的基石。虽然后者并非没有基本问题，但它为整个宇宙学观测提供了一个很好的唯象描述。然而，在认识到真空能量密度$ρ_{\textrm{vac}}$实际上是弯曲时空中量子场论中的一个“运行量”后，这种唯象描述得到了有趣的改进，$Λ$项的理论地位也发生了变化。几项研究表明，这种选择可以与具有严格$Λ$项的$Λ$ CDM竞争。所谓的“运行真空模型”（RVM）的特征实际上是一个随时间演化的$ρ_{\textrm{vac}}$，它是哈勃参数及其时间导数的一系列偶次幂。这种形式的动机是由重整化群参数在以前的工作。本文回顾了作者最近用绝热正则化方法对非极小耦合标量场重整化能量动量张量的详细计算。最后的结果是值得注意的：$ρ_{\textrm{vac}}(H)$采用了RVM的精确结构，即一个常数项加上一个动力学分量$\sim H^2$（在当前的宇宙中可能是可检测的），包括更高阶的效应$\mathcal{O}(H^4)$，这可能是在宇宙演化的早期阶段感兴趣。此外，最值得注意的是，这种重整化形式的$ρ_{\textrm{vac}}$不携带危险的条款成比例的$m^4$，四次幂的质量的领域，这是一个众所周知的来源非常大的贡献真空能量密度和直接负责微调的上下文中的CC问题。

英文摘要：

The cosmological constant term, $Λ$, in Einstein's equations has been for three decades a building block of the concordance or standard $Λ$CDM model of cosmology. Although the latter is not free of fundamental problems, it provides a good phenomenological description of the overall cosmological observations. However, an interesting improvement in such a phenomenological description and also a change in the theoretical status of the $Λ$-term occurs upon realizing that the vacuum energy density, $ρ_{\textrm{vac}}$, is actually a "running quantity" in quantum field theory in curved spacetime. Several works have shown that this option can compete with the $Λ$CDM with a rigid $Λ$term. The so-called, "running vacuum models" (RVM) are characterized indeed by a $ρ_{\textrm{vac}}$ which is evolving with time as a series of even powers of the Hubble parameter and its time derivatives. This form has been motivated by renormalization group arguments in previous works. Here we review a recent detailed computation by the authors of the renormalized energy-momentum tensor of a non-minimally coupled scalar field with the help of adiabatic regularization. The final result is noteworthy: $ρ_{\textrm{vac}}(H)$ takes the precise structure of the RVM, namely a constant term plus a dynamical component $\sim H^2$ (which may be detectable in the present universe) including also higher order effects $\mathcal{O}(H^4)$ which can be of interest during the early stages of the cosmological evolution. Besides, it is most remarkable that such renormalized form of $ρ_{\textrm{vac}}$ does not carry dangerous terms proportional to $m^4$, the quartic powers of the masses of the fields, which are a well-known source of exceedingly large contributions to the vacuum energy density and are directly responsible for fine tuning in the context of the CC problem.

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摘要：

英文摘要：

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