Effective cosmology from one-body operators in group field theory

TL;DR

This paper introduces a novel method to derive effective FLRW cosmology directly from group field theory by focusing on macroscopic observables, avoiding specific quantum state assumptions, and systematically including quantum effects.

Contribution

It develops a new approach to extract cosmological dynamics from GFT using one-body operators, providing a systematic expansion and relational formulation without fixing a clock.

Findings

Derives conditions for classical FLRW compatibility

Establishes a gauge fixing corresponding to cosmological variables

Includes quantum fluctuations in the effective dynamics

Abstract

We propose a new method for obtaining an effective Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmology from the quantum gravity dynamics of group field theory (GFT), based on the idea that an FLRW universe is characterised by a few macroscopic observables. Rather than relying on assuming a particular type of quantum state and computing expectation values in such a state, here we directly start from relations between macroscopic observables (defined as one-body operators) and formulate dynamics only for those observables. We apply the effective approach to constrained quantum systems (as developed by Bojowald and collaborators) to GFT, providing a systematic expansion in powers of $\hbar$. We obtain a kinematical phase space of expectation values and moments, which does not require an a priori choice of clock variable. We identify a gauge fixing of the system which corresponds to choosing one of the cosmological variables (with the role of extrinsic curvature) as a clock and which allows us to rewrite the effective dynamics in relational form. We show necessary and sufficient conditions for the resulting dynamics of expectation values to be compatible with those of classical FLRW cosmology and discuss the impact of quantum fluctuations.