Why Global Vacuum Energy Is Not an Admissible Degree of Freedom in a Non-Orientable Spacetime

Vacuum energy in standard cosmology is typically treated as a globally defined, orientation-invariant scalar that can function as a universal dynamical driver of late-time expansion. This work makes a constraint-first argument: in a globally non-orientable spacetime manifold, such a globally defined vacuum energy is not an admissible degree of freedom. The obstruction is topological, not observational or dynamical—global orientation reversal prevents the consistent definition of a single, path-independent vacuum energy density across the manifold. The paper makes no attempt to fit supernova, BAO, or CMB data, introduces no new fields or modified gravity terms, and does not dispute the empirical success of phenomenological ΛCDM fits. Instead, it isolates a prior structural question: whether a universal vacuum-energy scalar can be defined consistently in a non-orientable completion. The answer is negative. A direct consequence is a forced theoretical fork: either spacetime is globally orientable (permitting vacuum energy as a global explanatory primitive), or spacetime is non-orientable (in which case vacuum energy must be abandoned as a global degree of freedom and any apparent acceleration must be structural—emergent from spacetime geometry/topology—rather than substantive (sourced by an added bulk component).