Generalised effective cosmology from group field theory

TL;DR

This paper derives effective cosmological Friedmann equations from group field theory without mean-field approximation, revealing quantum corrections and state-dependent effects that resemble loop quantum cosmology and resolve singularities.

Contribution

It extends GFT-based cosmology by deriving general effective Friedmann equations applicable to various states, including interactions, without relying on mean-field assumptions.

Findings

Effective equations show quantum corrections similar to loop quantum cosmology.

Singularity resolution is achieved through these quantum corrections.

State-dependent terms influence the cosmological dynamics.

Abstract

We extend various recent results regarding the derivation of effective cosmological Friedmann equations from the dynamics of group field theory (GFT). Restricting ourselves to a single GFT field mode (or fixed values of Peter-Weyl representation labels), we first consider dynamics given by a quadratic Hamiltonian, which takes the form of a squeezing operator, and then add a quartic interaction that can be seen as a toy model for interactions in full GFT. Our derivation of effective Friedmann equations does not require a mean-field approximation; we mostly follow a general approach in which these equations in fact hold for any state. The resulting cosmological equations exhibit corrections to classical Friedmann dynamics similar to those of loop quantum cosmology, leading to generic singularity resolution, but also involve further state-dependent terms. We then specify these equations to various types of coherent states, such as Fock coherent states or Perelomov-Gilmore states based on the su(1,1) structure of harmonic quantum cosmology. We compute relative uncertainties of volume and energy in these states, clarifying whether they can be interpreted as semiclassical. In the interacting case, both analytical and numerical approximations are used to obtain modified cosmological dynamics. Our results clarify how effective cosmological equations derived from GFT can provide reliable approximations to the full dynamics.