Relational Time and Cyclic Cosmology in a Five-Dimensional Ultrahyperbolic Bulk

We propose the Temporal Cabinet, a five-dimensional geometric framework in whichgravity propagates through an extrinsic, non-compact time-like dimension, while standardquantum fields remain confined to their own intrinsic (3 + 1)-dimensional spacetimes. Theresulting ultrahyperbolic manifold, signature diag(−,+,+,+,−), induces a universal temporalscaling relation that governs relativistic kinematics without violating local Lorentzinvariance. Despite the presence of multiple time directions, canonical constraint reductionyields a closed first-class algebra and an essentially self-adjoint physical Hamiltonian,guaranteeing unitary quantum evolution and the strict absence of Ostrogradsky ghosts.Cosmologically, higher-curvature bulk dynamics drive a purely geometric, nonsingularbounce that natively replaces slow-roll inflation. The extrinsic temporal scaling generates anearly scale-invariant scalar power spectrum (n_s ≈ 0.96), parametrically suppresses tensormodes (r ≪ 10^−2), and predicts a constant equilateral non-Gaussianity (f^equil_NL ≈ −0.33). Furthermore, the framework’s symmetry-protected zero total energy constraint mathematicallyneutralises the 10^120 vacuum energy divergence. By elevating time to a relational bulkdimension, the theory provides a unified, purely classical/semi-classical resolution to the initialsingularity, dark energy, dark matter kinematics, and the matter-antimatter asymmetry,entirely bypassing the need for discrete quantum gravity or exotic particles.