Integrating Modulus Time with String Theory Dualities Dynamical Moduli and Cyclic Cosmology

Abstract We present a rigorous formulation of Modulus Time, in which physical evolution depends on the magnitude of time rather than its orientation, and embed it consistently into string theory. Modulus Time is derived as an emergent relational degree of freedom arising from a Hamiltonian constraint, rather than postulated. We demonstrate its compatibility with string worldsheet dynamics, compactification moduli, T-duality, and string gas cosmology. Lorentz invariance and causality are shown to emerge locally, while a global time-reversal symmetry is preserved. The resulting framework naturally yields a non-singular cyclic cosmology with mirrored entropy evolution and leads to testable predictions for cosmological observables.