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arXiv · 2201.02575

The spatial Functional Renormalization Group and Hadamard states on cosmological spacetimes

Rudrajit Banerjee·Max Niedermaier
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Abstract

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). The state-dependent infrared behavior of the flow is investigated for States of Low Energy, which are Hadamard states deemed to be viable vacua for a pre-inflationary period. A simple time-dependent infrared fixed point equation (resembling that in Minkowski space) arises for any scale factor, with analytically computable corrections coding the non-perturbative ramifications of the Hadamard property in the infrared.

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Rudrajit Banerjee, Max Niedermaier. 2022-01-07. The spatial Functional Renormalization Group and Hadamard states on cosmological spacetimes. https://doi.org/10.1016/j.nuclphysb.2022.115814

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