Curvature, Memory and Emergent Time in Cosmological Dynamics

Abstract We present a covariant geometric extension of General Relativity incorporatingcurvature–memory effects parametrized by the coefficients α, β, and γ. The resultingtheory preserves second–order field equations and remains free of ghost instabilitieswithin a well–defined low-energy effective field theory regime. A repulsive curvaturecore proportional to a−6 replaces the initial cosmological singularity with a smooth,nonsingular bounce. In addition, a geometric slip term proportional to ˙H introducesirreversible curvature dynamics, giving rise to an intrinsic and monotonic emergenttime variable τ (or equivalently a geometric phase θ) without the introduction ofadditional matter clocks. The combined effect of curvature regularization and geometricdissipation yields dynamically stable cosmological solutions and a well-defined arrow oftime. Finally, we briefly discuss the implications of this framework for early-universephenomenology, including possible implications for early structure formation that arequalitatively compatible with recent JWST observations.