标题： 在FLRW时空中的QFT真空演化：由量子化物质场决定的$ρ_{\rm vac}(H)$的动力学 显示英文标题

标题： Running vacuum in QFT in FLRW spacetime: The dynamics of $ρ_{\rm vac}(H)$ from the quantized matter fields

摘要： Phenomenological work in the last few years has provided significant support to the idea that the vacuum energy density (VED) is a running quantity with the cosmological evolution and that this running helps to alleviate the cosmological tensions afflicting the $\Lambda$CDM. On the theoretical side, recent devoted studies have shown that the properly renormalized $\rho_{\rm vac}$ in QFT in FLRW spacetime adopts the "running vacuum model" (RVM) form. While in three previous studies by two of us (CMP and JSP) such computations focused solely on scalar fields non-minimally coupled to gravity, in the present work we compute the spin-$1/2$ fermionic contributions and combine them both. The calculation is performed using a new version of the adiabatic renormalization procedure based on subtracting the UV divergences at an off-shell renormalization point $M$. The quantum scaling of $\rho_{\rm vac}$ with $M$ turns into cosmic evolution with the Hubble rate, $H$. 因此，“宇宙学常数”$\Lambda$在我们的框架中表现为在任意给定的时刻$H$附近$8\pi G(H)\rho_{\rm vac}(H)$的几乎恒定值，其中$G(H)$是引力耦合常数，它也是变化的（尽管非常微弱，以对数形式）。 我们发现当前真空能量密度（VED）的演化为 $\delta \rho_{\rm vac}(H)\sim \nu_{\rm eff}\, m_{\rm Pl}^2 \left(H^2-H_0^2 \right)\ (|\nu_{\rm eff}|\ll 1)$。 系数$\nu_{\rm eff}$收到来自所有量子化场（包括玻色子和费米子）的贡献。 值得注意的是，还存在更高次幂${\cal O}(H^{6})$，它们可以在早期宇宙中引发暴涨。 最后，真空的状态方程（EoS）也受到玻色子和费米子场的量子修正，使其偏离 -1。 令人震惊的结果是，如今量子真空的状态方程可能有效表现为暗能量 Quintessence。 显示英文摘要

摘要： Phenomenological work in the last few years has provided significant support to the idea that the vacuum energy density (VED) is a running quantity with the cosmological evolution and that this running helps to alleviate the cosmological tensions afflicting the $\Lambda$CDM. On the theoretical side, recent devoted studies have shown that the properly renormalized $\rho_{\rm vac}$ in QFT in FLRW spacetime adopts the "running vacuum model" (RVM) form. While in three previous studies by two of us (CMP and JSP) such computations focused solely on scalar fields non-minimally coupled to gravity, in the present work we compute the spin-$1/2$ fermionic contributions and combine them both. The calculation is performed using a new version of the adiabatic renormalization procedure based on subtracting the UV divergences at an off-shell renormalization point $M$. The quantum scaling of $\rho_{\rm vac}$ with $M$ turns into cosmic evolution with the Hubble rate, $H$. As a result the "cosmological constant" $\Lambda$ appears in our framework as the nearly sustained value of $8\pi G(H)\rho_{\rm vac}(H)$ around (any) given epoch $H$, where $G(H)$ is the gravitational coupling, which is also running, although very mildly (logarithmically). We find that the VED evolution at present reads $\delta \rho_{\rm vac}(H)\sim \nu_{\rm eff}\, m_{\rm Pl}^2 \left(H^2-H_0^2 \right)\ (|\nu_{\rm eff}|\ll 1)$. The coefficient $\nu_{\rm eff}$ receives contributions from all the quantized fields, bosons and fermions. Remarkably, there also exist higher powers ${\cal O}(H^{6})$ which can trigger inflation in the early universe. Finally, the equation of state (EoS) of the vacuum receives also quantum corrections from bosons and fermion fields, shifting its value from -1. The striking consequence is that the EoS of the quantum vacuum may nowadays effectively appears as quintessence.