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.

中文翻译：

---

来自群场论的广义有效宇宙学

我们扩展了有关从群场论 (GFT) 动力学推导有效宇宙学弗里德曼方程的各种最新结果。将自己限制为单个 GFT 场模式（或 Peter-Weyl 表示标签的固定值），我们首先考虑由二次哈密顿量给出的动力学，它采用挤压算子的形式，然后添加一个四次相互作用，可以看作用于完全 GFT 交互的玩具模型。我们对有效弗里德曼方程的推导不需要平均场近似；我们大多遵循一种通用方法，其中这些方程实际上适用于任何状态。由此产生的宇宙学方程表现出对经典弗里德曼动力学的修正，类似于圈量子宇宙学的修正，导致通用奇点分辨率，但还涉及进一步的状态相关项。然后，我们将这些方程指定为各种类型的相干态，例如基于谐波量子宇宙学的 su(1,1) 结构的 Fock 相干态或 Perelomov-Gilmore 态。我们计算这些状态下体积和能量的相对不确定性，阐明它们是否可以解释为半经典。在相互作用的情况下，分析和数值近似都用于获得修改后的宇宙动力学。我们的结果阐明了从 GFT 导出的有效宇宙学方程如何为完整动力学提供可靠的近似值。我们计算这些状态下体积和能量的相对不确定性，阐明它们是否可以解释为半经典。在相互作用的情况下，分析和数值近似都用于获得修改后的宇宙动力学。我们的结果阐明了从 GFT 导出的有效宇宙学方程如何为完整动力学提供可靠的近似值。我们计算这些状态下体积和能量的相对不确定性，阐明它们是否可以解释为半经典。在相互作用的情况下，分析和数值近似都用于获得修改后的宇宙动力学。我们的结果阐明了从 GFT 导出的有效宇宙学方程如何为完整动力学提供可靠的近似值。