Renormalizing the vacuum energy in cosmological spacetime: implications for the cosmological constant problem

Understand

The renormalization of the vacuum energy in quantum field theory (QFT) is usually plagued with theoretical conundrums related not only with the renormalization procedure itself, but also with the fact that the final result leads usually to very large (finite) contributions incompatible with the measured value of $\Lambda$ in cosmology.

• Herein, we compute the zero-point energy (ZPE) for a nonminimally coupled (massive) scalar field in FLRW spacetime using the off-shell adiabatic renormalization technique employed in previous work.
• The general off-shell result yields a smooth function $\rho_{\rm vac}(H)$ made out of powers of the Hubble rate and/or of its time derivatives involving different (even) adiabatic orders $\sim H^N$ ($N=0,2,4,6,...)$, i.e.
• it leads, remarkably enough, to the running vacuum model (RVM) structure.