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.
Highlights
Spacetime singularities are among the most spectacular predictions of classical general relativity
Our aim was to present a general perspective on the derivation of reliable effective Friedmann equations from given quantum dynamics of a GFT model, building on various recent developments in the derivation of effective cosmological dynamics from GFT
While there are arguments suggesting the dynamical emergence of a regime dominated by a single ield mode in GFT, showing such an emergence in models of interest for four-dimensional quantum gravity remains an outstanding challenge
Summary
Spacetime singularities are among the most spectacular predictions of classical general relativity. These are interpreted as effective Friedmann equations derived from the GFT condensate dynamics These steps were irst fully implemented in [23, 24] where it was shown how such effective Friedmann equations, for a wide class of GFT models and under various simplifying assumptions, are consistent with the classical Friedmann equations at large volume while showing a bouncing behaviour at high densities very similar to the one in LQC. These effective Friedmann equations can reproduce the preferred ‘improved dynamics’ form of LQC [25] whose derivation from Hamiltonian formulations of LQG is a largely outstanding challenge [10] These very promising results for effective cosmological dynamics from GFT relied on assuming the emergence of a condensate regime in which the mean-ield approximation is valid and GFT interactions are subdominant with respect to the quadratic (kinetic) term. Perelomov–Gilmore states that can be thought of as elements of a GFT-like Fock space do not admit such a semiclassical interpretation and are disfavoured for GFT cosmology
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