Finite Universe and Terminal Sliding Dynamics: A Quantum Perspective

Singularities and abrupt boundaries challenge the completeness of standard cosmological models rooted in General Relativity (GR). These unresolved issues, such as the Big Bang singularity and black hole interiors, highlight the need for modifications in extreme curvature regimes. In this work, we propose a minimal yet effective extension to the Friedmann equations, introducing two corrective terms: a quantum correction proportional to 1/a6, which dominates in high-curvature regimes, and a dynamic smoothing term proportional to ˙a2, which stabilizes geodesic trajectories. These corrections regularize curvature invariants, ensure geodesic continuity, and lead to a smooth, non-singular expansion. Numerical simulations show that the corrected model aligns with key cosmological observations, including the Cosmic Microwave Background (CMB), large-scale structure, and gravitational wave spectra. Moreover, it predicts distinct observational signatures, such as modifications in the matter power spectrum and high-frequency features in the gravitational wave background, testable with upcoming missions like CMB-S4, Euclid, and LISA. This framework offers a consistent and testable alternative to current paradigms, bridging theoretical advancements with observational physics. [email protected]