= Scale-independent matter suppression by a coasting fluid
The matter equation in the barotropic matter-string model contains no wavenumber. Growing initial data therefore evolve as $\delta_c(k,\eta)=A_kD(\eta)$ with the same $D$ for every mode. For regular adiabatic modes initially outside the horizon during <matter domination>, $A_k$ is proportional to $k^2$ times the primordial curvature amplitude. The density-per-curvature transfer is consequently proportional to $k^2D(\eta)$ for modes entering after equality. Factoring out both $k^2$ and $D$ gives a constant shape transfer on those scales. Comparing with continued matter-era growth instead introduces the common suppression $D(\eta)/\eta$, not a new wavenumber dependence.
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