 Cold-matter growth in a matter-coasting-fluid universe

In a spatially flat universe containing separately conserved pressureless matter and a coasting fluid with $w=-1/3$, the ratio $\eta ={\rho }_s/{\rho }_m$ is proportional to the scale factor. If the coasting component is modeled by the barotropic fluid perturbation equations with no anisotropic stress, its contribution to the trace gravitational source vanishes because $1+3w=0$. The matter growing mode isA decaying solution is $D_{-}=\sqrt{1+\eta }/{\eta }^{3/2}$. The reduction of order formula with integrating factor ${\eta }^{3/2}\sqrt{1+\eta }$ produces the integral solution. It has $D=\eta [1-4\eta /7+O({\eta }^2)]$ during matter domination and tends to $5/2$ during coasting-fluid domination. Thus growth freezes rather than continuing in proportion to the scale factor. The background geometry is flat despite the same background expansion law as an open dust universe.