A Modulated Two-Scalar Framework for Stable Non-Topological Solitons: Derivative Coupling, Spectral Stability, and Cosmological Bounds

We propose a covariant two-scalar field theory in which a dimensionless modulating scalar $\lambda(x)$ controls the kinetic, mass, and potential sectors of a complex scalar field $\Psi(x)$ through a $(1-\lambda)$ prefactor. The model possesses an exact, field-dependent $U(1)$ Noether current and a covariantly conserved stress-energy tensor. We demonstrate the existence of localized non-topological soliton (Q-ball) solutions and establish their classical orbital stability within the Grillakis--Shatah--Strauss (GSS) framework: the unconstrained radial Hessian operator possesses exactly one negative dilation mode ($n^- = 1$), which is rigorously projected out on the constant-charge manifold by the Vakhitov--Kolokolov condition $dQ/d\omega < 0$. We verify this condition analytically via an explicit intermediate derivation in the thin-wall regime and numerically via adaptive shooting. Real-time hyperbolic integrations confirm the non-linear stability and radiation damping of finite radial perturbations. An explicit bare mass for $\lambda$ guarantees exponential Yukawa screening, shielding external long-range fifth forces. We formulate the perturbation scattering theory of scalar fluctuations off the non-topological background, demonstrating how the advective gradient coupling dresses the standard background potential barrier. In an expanding FLRW background, we delineate between the unfragmented homogeneous oscillating condensate behaving as cold dark matter ($\langle w \rangle \approx 0$) and the fragmented soliton phase generated via parametric resonance bands, deriving observational cluster collision bounds that constrain the macroscopic soliton parameter space.