Loop quantum bounce leaves a tiny but calculable mark on the CMB

Starting from Loop Quantum Cosmology, these calculations extend the classical phase space with quantum moments—dispersions and correlations—to track how a cosmic bounce alters scalar perturbations. In the test-field limit and flat potential, the Mukhanov-Sasaki variable satisfies a third-order equation whose bounce-induced correction shifts the spectral index by δnₛ ~ 6(kℓ_Pl)⁶, safely invisible to present instruments. A numerical treatment of the fully coupled system uncovers a more interesting feature: gravitational quantum moments damp scalar amplitudes after the bounce, while cross-sector correlations amplify modes and trigger ultraviolet instabilities that expose the breakdown of the second-order moment truncation.