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

Understand

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 $M$.