A Cyclic Bounce Cosmology with Higher-Order Nonlocal Curvature and Ramanujan-Form Time Gravity

Aiming at the theoretical defects of classical general relativity, including singularity divergence, dark matter puzzles, cosmic initial boundary conditions and fixed spacetime dimensions, this paper constructs a self‑consistent gravitational cosmological model incorporating Ramanujan modular‑form time gravity, higher‑order nonlocal curvature, fermion field coupling, topological fluctuations, Kaluza‑Klein compactification and cyclic bounce dynamics.The main derivations are as follows: 1. Higher‑order nonlocal curvature terms R^{2}, R_{\mu\nu}^{2} and R\square R are introduced to regularize spacetime singularities and form a finite spacetime core. 2. A time‑gravity field equation is constructed via Ramanujan theta functions, establishing the full dynamics of the time dimension. 3. Fermion fields in curved spacetime are fully incorporated, with direct coupling between fermions and time gravity derived. 4. Quantum‑gravitational equations of motion with mass‑curvature high‑energy corrections are established, completing the transition from classical to quantum cyclic bounce cosmology.