Finite Universe and Terminal Sliding Dynamics: A Quantum Perspective-Quantum-Corrected Friedmann Dynamics

I propose a novel cosmological model that introduces a dynamic sliding term into the standard Friedmann–Lemaître–Robertson–Walker (FLRW) equations. This geometric correction, derived from a variational principle, acts as a curvature-sensitive feedback mechanism that regulates the Hubble parameter's growth and ensures a singularity-free evolution of the early universe. Unlike inflationary or bounce-based models, our approach does not require scalar fields, extra dimensions, or discrete quantum structures. The effective Lagrangian includes three key contributions: a quantum geometric term dominant at small scales, a thermodynamic damping term proportional to the expansion rate, and a sliding term linked to the time derivative of the Hubble parameter. The resulting second-order nonlinear field equations are solved numerically using an adaptive RK45 scheme. Our simulations demonstrate that the scale factor \( a(t) \) evolves smoothly from Planck-scale initial conditions, with bounded curvature and a finite Hubble parameter at all times. The model naturally interpolates between quantum-dominated and classical regimes without singular behavior. Observable signatures include early-universe gravitational wave suppression, potential deviations in the tensor-to-scalar ratio, and scale-dependent modulations in the CMB power spectrum—offering clear opportunities for experimental testing with next-generation cosmological probes such as CMB-S4, LiteBIRD, and LISA. This framework illustrates how minimal geometric extensions to general relativity can resolve deep cosmological puzzles while remaining testable and theoretically grounded. [email protected]