We extend the DFH framework of expansion without cosmological constant to the linear perturbation regime. A canonical field ϕ with scale function g(t) unifies the background dynamics from the Big Bang to today. Here we show that the same scaling law governs matter perturbation growth, without introducing independent dark energy components. We derive the modified growth equation ¨δ + 2H(t) ˙δ = 4πGeff(t)ρmδ, where Geff(t) inherits the evolution of g(t). The model predicts a growth rate fσ8(z) consistent with RSD data, suppresses power at sub-Mpc scales solving the missing satellites problem, and generates flat rotation curves without additional cold dark matter. With a single free parameter f∗, DFH reproduces the structure formation history from recombination to z = 0, offering a complete cosmology of background + perturbations with a single physical cause.