Noether Symmetries in Scalar--Vector--Two-Form Cosmology with a Topological BF Interaction

Abstract

We study a canonical scalar field coupled to isotropic triplets of Abelian one-forms and two-forms through scalar-dependent kinetic functions and a constant topological $BF$ interaction. By retaining the lapse in the homogeneous reduction, we recover the Friedmann constraint and identify a sufficient domain in which all twelve physical modes have positive kinetic terms and luminal high-frequency propagation. A separate exponential model admits an accelerating mixed solution with $a\propto t^2$, nonzero asymptotic form fractions, and bounded normalized linear perturbations. For the Noether analysis, we choose a quadratic effective potential in flat minisuperspace coordinates and solve the zero-boundary determining equations. The canonical scalar potential is hyperbolic-squared or exponential, rather than a power law in the scalar field. The causal character of the potential coordinate separates three branches: Branch I admits a de Sitter limit, Branch II cannot sustain acceleration on regular future-complete expanding trajectories, and Branch III gives an exact solution with both form sectors active and late expansion $a\propto t^{4/3}$. Comparisons with consistent uncoupled and reduced-field limits separate the form contributions from the scalar-driven acceleration. The $BF$ term changes the finite-time exchange between the form sectors but supplies no direct negative-pressure source.