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arXiv 2005.03164gr-qcastro-ph.COhep-phhep-th
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弯曲时空中量子场论中的运行真空：不带$\sim m^4$项的$ρ_{vac}$重整化

Running vacuum in quantum field theory in curved spacetime: renormalizing $ρ_{vac}$ without $\sim m^4$ terms

Cristian Moreno-Pulido, Joan Sola

备注：
Matches the published version
发表信息：
Eur. Phys. J. C 80, 692 (2020)
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摘要：

爱因斯坦方程中的$Λ$ -项是宇宙学“和谐”$Λ$ CDM模型的基本组成部分。尽管该模型并非没有基本问题，但它们也没有被任何替代暗能量的提议所规避。这里我们坚持PDMATHAMM项，但我们认为它可以是弯曲时空中量子场论（QFT）中的一个“运行量”。大量的唯象学研究表明，这种选择可以与具有严格宇宙学项的$Λ$ CDM竞争。所谓的“运行真空模型”（RVM）的特征是真空能量密度$ρ_{vac}$，它是哈勃参数及其时间导数的一系列（偶）幂。这种理论形式是由一般重整化群的论点所激发的，看起来似乎是合理的。在这里，我们将进一步讨论FLRW时空中QFT中RVM结构的起源。我们计算重整化能量动量张量的绝热正则化过程的帮助下，发现它本质上导致RVM形式。这意味着$ρ_{vac}(H)$演化为一个常数项加上动力学分量${\cal O}(H^2)$和${\cal O}(H^4)$，后者只与早期宇宙有关。然而，重整化的$ρ_{vac}(H)$不携带与场的质量的四次幂（$\sim m^4$）成比例的危险项，这些项是非常大的贡献的众所周知的来源。目前，$ρ_{vac}(H)$主要是由附加常数项控制的，并伴随着一个温和的动力学分量$\sim νH^2$（$|ν|\ll1$），它模仿了经典.

英文摘要：

The $Λ$-term in Einstein's equations is a fundamental building block of the `concordance' $Λ$CDM model of cosmology. Even though the model is not free of fundamental problems, they have not been circumvented by any alternative dark energy proposal either. Here we stick to the $Λ$-term, but we contend that it can be a `running quantity' in quantum field theory (QFT) in curved spacetime. A plethora of phenomenological works have shown that this option can be highly competitive with the $Λ$CDM with a rigid cosmological term. The, so-called, `running vacuum models' (RVM's) are characterized by the vacuum energy density, $ρ_{vac}$, being a series of (even) powers of the Hubble parameter and its time derivatives. Such theoretical form has been motivated by general renormalization group arguments, which look plausible. Here we dwell further upon the origin of the RVM structure within QFT in FLRW spacetime. We compute the renormalized energy-momentum tensor with the help of the adiabatic regularization procedure and find that it leads essentially to the RVM form. This means that $ρ_{vac}(H)$ evolves as a constant term plus dynamical components ${\cal O}(H^2)$ and ${\cal O}(H^4)$, the latter being relevant for the early universe only. However, the renormalized $ρ_{vac}(H)$ does not carry dangerous terms proportional to the quartic power of the masses ($\sim m^4$) of the fields, these terms being a well-known source of exceedingly large contributions. At present, $ρ_{vac}(H)$ is dominated by the additive constant term accompanied by a mild dynamical component $\sim νH^2$ ($|ν|\ll1$), which mimics quintessence.

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