# Fakeons and the classicization of quantum gravity: the FLRW metric

## TL;DR

This paper explores how fakeons can be used to quantize higher derivative theories of quantum gravity and examines the classicalization process, especially in the context of the FLRW metric, highlighting cases with exact and approximate projections.

## Contribution

It introduces a perturbative approach to classicalize quantum gravity theories via fakeons and analyzes their properties within the FLRW metric framework, identifying cases with exact and approximate projections.

## Key findings

- Fakeon projection can be handled exactly for radiation and vacuum energy.
- The classical limit often shares features with the quantum theory, including non-perturbative effects.
- Complete, exact field equations are generally not obtainable due to asymptotic series.

## Abstract

Under certain assumptions, it is possible to make sense of higher derivative theories by quantizing the unwanted degrees of freedom as fakeons, which are later projected away. Then the true classical limit is obtained by classicizing the quantum theory. Since quantum field theory is formulated perturbatively, the classicization is also perturbative. After deriving a number of properties in a general setting, we consider the theory of quantum gravity that emerges from the fakeon idea and study its classicization, focusing on the FLRW metric. We point out cases where the fakeon projection can be handled exactly, which include radiation, the vacuum energy density and the combination of the two, and cases where it cannot, which include dust. Generically, the classical limit shares many features with the quantum theory it comes from, including the impossibility to write down complete, "exact" field equations, to the extent that asymptotic series and nonperturbative effects come into play.