Curvature, Memory and Emergent Time in Cosmological Dynamics

We present a covariant geometric extension of General Relativity formulated within a controlled effective field theory framework. The gravitational action is supplemented by curvature-dependent operators parametrized by three coefficients α, β, and γ, chosen such that the resulting field equations remain second order in time derivatives and free of Ostrogradsky instabilities. In a homogeneous and isotropic cosmological background, the modified dynamics generically replaces the classical Big Bang singularity with a smooth, nonsingular bounce driven by a repulsive curvature core proportional to a−6. A distinctive feature of the framework is the presence of a geometric slip term proportional to H˙, which encodes curvature-memory effects at the level of the background evolution without introducing additional propagating degrees of freedom. This term dynamically correlates the expansion rate with its temporal variation, leading to effective ultraviolet damping and enhanced dynamical stability across the high-curvature regime. As a consequence, the cosmological solutions admit the definition of an intrinsic relational time variable that is strictly monotonic throughout the evolution, including across the bounce. The emergent temporal ordering arises purely from geometric dynamics and does not rely on matter clocks, nonlocality, or fundamental violations of time-reversal or CPT symmetry. We discuss the consistency of the framework within its effective field theory domain of validity and comment on its implications for the conceptual problems of singularity resolution and the emergence of time in cosmology.