AI 中文总结
该研究从群场论量子引力的基础动力学出发，推导了涵盖宇宙早晚期的有效标量场理论，得到带量子引力修正的FLRW时空标量场动力学，其非均匀性波动方程可作为识别量子引力信号的途径。
AI 中文摘要
我们从完全关系框架下的基础量子引力动力学出发，推导了群场论（Group Field Theory, GFT）凝聚态宇宙学中物质的有效标量场理论，该理论涵盖了宇宙早期和晚期阶段。 underlying量子几何的集体流体动力学使我们能够重构物质与几何的均匀宇宙动力学，以及非均匀的局域场论描述。时空的局域化是相对于物质参考框架以关系方式定义的。在均匀层面，我们得到了由凝聚态选定的涌现FLRW时空上的修正标量场理论，该理论在晚期广义相对论 regime下恢复了无质量标量场的标准动力学，同时在宇宙反弹附近保留量子引力修正。在微扰层面，标量非均匀性满足带有 underlying量子引力微观结构特征的有效波动方程，在宇宙早期 regime下，该方程呈现出兼具色散和耗散贡献的修正色散关系。这些修正为直接从基础量子引力框架识别量子引力的唯象学信号提供了具体途径。
英文摘要
We derive an effective scalar field theory for matter in group field theory condensate cosmology, starting from the fundamental quantum-gravity dynamics in a fully relational framework and encompassing both early- and late-universe regimes. The collective hydrodynamics of the underlying quantum geometry allows us to reconstruct both the homogeneous cosmological dynamics of matter and geometry and an inhomogeneous local field-theory description. Localization in space and time is defined relationally with respect to a material reference frame. At the homogeneous level, we obtain a modified scalar field theory on the emergent FLRW spacetime selected by the condensate. It recovers the standard dynamics of a massless scalar field in the late-time general-relativistic regime while retaining quantum-gravity corrections near the cosmological bounce. At the perturbative level, scalar inhomogeneities obey an effective wave equation that carries signatures of the underlying quantum-gravity microstructure. In the early-universe regime, this equation exhibits a modified dispersion relation with both dispersive and dissipative contributions. These corrections provide a concrete avenue for identifying phenomenological signatures of quantum gravity directly from a fundamental quantum-gravity framework.
