DFH Cosmology: Unifying Inflation, CMB, and Dark Energy via a Time-Varying Coupling g(t)

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.