Homogeneous cosmological models and topology
Abstract: Spatially homogeneous (SH) cosmological models are central to our understanding of the Big Bang singularity, the late-time isotropisation and the role of matter, and they provide a key framework for testing global anisotropy with CMB observations. Meanwhile, Thurston’s classification of three-manifolds has shown that spatial topology can strongly constrain the geometry and dynamics of SH spacetimes. This close connection between topology and SH models makes it natural to study them in topo-GR, a parameter-free modification of general relativity in which the field equations include a topology-dependent term. I will present how spatially homogeneous (Bianchi–Kantowski–Sachs) cosmologies are formulated in this framework and highlight how the dynamics differ from general relativity, briefly discussing one of the main perspectives: the implications for the quantisation of inflation.