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 ${\delta }_c(k,\eta )=A_{k}D(\eta )$ 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 $k^{2}D(\eta )$ 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.