On the Hilbert Space in QTIP Cosmology

This paper proposes a mathematical approach for applying a single Hilbert space (HS) in QTIP Cosmology. Based on the mathematical structure of composite systems in quantum mechanics (QM) and quantum information theory (QIT), it examines the correspondence of superposition, normalization and the Born Rule, entanglement, subsystem measurement statistics, and generalization to N-particle systems. Rather than constructing a new composite Hilbert space through tensor products of independent Hilbert spaces, QTIP Cosmology proposes defining a relational subset HS within a single Hilbert space based on the boundary conditions among QIF_Is. This approach does not exclude the mathematical structures of QM/QIT, but proposes an alternative framework for applying them within a single Hilbert space.