Global Phase-Space Dynamics and Quantum Cosmic Bounce

We present a rigorous, first-principles derivation of emergent dark energy and cosmic singularity resolution operating within the framework of covariant Madelung quantum hydrodynamics. By applying a variational principle to the action of a relativistic complex scalar field without ad-hoc algebraic constraints, we extract the exact energy-momentum tensor. Within a spatially flat Friedmann-Lemaitre-Robertson-Walker background, the continuous temporal evolution of the quantum fluid amplitude generates a dynamic, non-local stress component via the relativistic Bohmian quantum potential Q. We perform a rigorous global phase-space stability analysis across both the expanding branch (where Hubble parameter is greater than zero) and the contracting branch (where Hubble parameter is less than zero). For the expanding branch, we prove the existence of a unique, mathematically stable de Sitter node attractor (where Hubble parameter equals H_0 and its time derivative equals zero) where the effective equation of state parameter asymptotically approaches minus one, naturally mitigating the vacuum zero-point fine-tuning problem. For the contracting branch, we demonstrate that the sharp amplification of the fluid density gradient triggers an immense quantum repulsion limit at Hubble parameter equals minus H_0. This non-local quantum pressure completely halts gravitational collapse at a non-zero minimum radius, establishing a non-singular, symmetric cosmic bounce and ensuring physical variables remain bounded. This framework offers a unified, purely hydrodynamic origin for the dark sector while eliminating physical singularities from spacetime.