The spatial Functional Renormalization Group and Hadamard states on cosmological spacetimes

Understand

A spatial variant of the Functional Renormalization Group (FRG) is introduced on (Lorentzian signature) globally hyperbolic spacetimes.

• Through its perturbative expansion it is argued that such a FRG must inevitably be state dependent and that it should be based on a Hadamard state.
• A concrete implementation is presented for scalar quantum fields on flat Friedmann-Lema\^{i}tre spacetimes.
• The universal ultraviolet behavior of Hadamard states allows the flow to be matched to the one-loop renormalized flow (where strict removal of the ultraviolet cutoff requires a tower of potentials, one for each power of the Ricci scalar).