Vacuum energy and renormalization of the field-independent term

Due to its construction, the nonperturbative renormalization group (RG) evolution of constant, field-independent term (which is constant with respect field variations but depends on RG scale $k$) requires special care within Functional Renormalization Group (FRG) approach. In several instances, potential has no physical meaning. However, there are cases where it receives important applications. low dimensions ($d=1$), in a quantum mechanical model, this associated ground-state energy anharmonic oscillator. higher ($d=4$), identical $\Lambda$ Einstein equations and plays role cosmic inflation. Thus, statistical theory, flat space, could be free energy, while curved naturally cosmological constant. It known that one use subtraction method for oscillator $d=1$ remove $k^2$ appears flow high-energy (UV) limit order recover correct results energy. The needed because Gaussian fixed point missing once included. if there, further required. Here, we propose $k^4$ terms UV scaling $d=4$ term. Finally, comments application our models provided.