On the Impossibility of Interpreting Global Cosmological Models as Locally Defined Physical Quantities

This paper examines whether the content of global cosmological models can be interpreted as locally defined physical quantities. Locality is formulated in a minimal and mathematically closed manner using the notion of metric germs, identifying local quantities as those fully determined by arbitrarily small spacetime neighborhoods. A necessary criterion for local representability is established in terms of invariance under local isomorphism. Explicit examples are constructed of cosmological spacetimes that are locally indistinguishable at every point yet globally non-isomorphic, including flat FLRW models with different spatial topologies. These examples show that standard global model quantities such as spatial topology, global integrals, and interpretations of the scale factor as the expansion of space as a whole violate the criterion for local representability. The resulting impossibility is not empirical or interpretative but definitional, reflecting a mismatch of domains rather than observational limitation. Consequences for discussions of superluminal expansion and causality are analyzed. The analysis clarifies the status of global cosmological models as representational structures rather than collections of locally defined physical observables.