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

Understand

The $\Lambda$-term in Einstein's equations is a fundamental building block of the `concordance' $\Lambda$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 $\Lambda$-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 $\Lambda$CDM with a rigid cosmological term.