Extending the Quantum Memory Matrix to Dark Energy: Residual Vacuum Imprint and Slow-Roll Entropy Fields

We extend the Quantum Memory Matrix (QMM) framework—previously shown to unify gauge interactions and reproduce cold dark matter phenomenology—to account for the observed late-time cosmic acceleration. In QMM, each Planck-scale cell carries a finite-dimensional Hilbert space of quantum imprints. We show that (1) once local unitary evolution saturates the available micro-states, a uniform residual “vacuum-imprint energy” remains; its stress–energy tensor is of pure cosmological-constant form, with magnitude suppressed by the cell capacity, naturally yielding ρΛ≃(2×10−3eV)4; and (2) if imprint writes continue but are overdamped by cosmic expansion, the coarse-grained entropy field S(t) undergoes slow-roll evolution, generating an effective equation of state w(z)≈−1+O(10−2) that is testable by DESI, Euclid, and Roman. We derive the modified Friedmann equations, linear perturbations, and joint constraints from Planck 2018, BAO, and Pantheon +, finding that the QMM imprint model reproduces the observed TT, TE, and EE spectra without introducing additional free parameters and alleviates the H0 tension while remaining consistent with the large-scale structure. In this picture, dark matter and dark energy arise as gradient-dominated and potential-dominated limits of the same underlying information field, completing the QMM cosmological sector with predictive power and internal consistency.