Quantum Simulation of TSTU Scalar Field Dynamics: Mapping Aetheron Stability onto Dipolar Quantum Droplets

We establish a formal mapping between the scalar field potential of the Unified Tensor-Scalar Theory (TSTU) and the Gross-Pitaevskii dynamics of dipolar Bose-Einstein condensates, within explicitly documented symmetry constraints (U(1) vs Z_2), with structural divergences quantified in Section 2. The quartic-sextic structure of the Δ M field potential maps onto two-body and three-body interaction terms, with stable solitonic configurations (Aetherons) finding a controlled analogue in quantum droplets. Using cosmological parameters constrained by Pantheon+ observations (β = 0.095), we derive the dimensionless stability ratio α = λ_4^2 / (λ_6 m^2) and identify the corresponding Feshbach resonance window in ¹⁶⁴Dy (B ∈ [150, 207] G at n ~ 10¹⁴ cm⁻³). Numerical results reveal an inverse trade-off between structural robustness and maximum storable charge. This work provides a controlled laboratory analogue to probe dark sector-inspired scalar dynamics at sub-gravitational scales, providing a falsifiable benchmark for the internal consistency of the TSTU scalar sector.