PT-Symmetric Quaternionic Spacetime: Phenomenological Insights from a String-Inspired Geometric Model

We propose a PT-symmetric quaternionic extension of four-dimensional spacetime, inspired by string theory and non-Hermitian geometry. The metric includes an imaginary component derived from a coordinate-dependent B-field structure, motivated by SU(2) gauge symmetry in type-IIB flux compactifications. A simplified toy model on a torus demonstrates how T-duality maps internal flux into this rotational B-field.Using standard string-theoretic effects such as large-volume suppression and warping, the model naturally reduces the string-scale parameter to an effective value consistent with galactic observations. A single dimensionless coupling parameter, ε ≈ 2.2, allows the model to simultaneously reproduce the Planck-2018 dark energy density and flatten the rotation curves of 175 SPARC galaxies, achieving a total reduced chi-squared near 446. The model outperforms the ΛCDM halo fit in approximately 40% of the cases.This framework is linearly stable, respects combined parity and time reversal, and supports a spectral-action interpretation. It offers a coherent and minimal-parameter mechanism to unify dark energy and galactic dynamics through a common geometric origin.