Linear growth equation

For pressureless matter on subhorizon scales, the linear growth factor obeysThe second term is dilution by cosmic expansion, while the final term drives Jeans instability.

Replacing the self-gravity term in the matter growth equation by $(1-f)4\pi G{\bar{\rho }}_{m}D$, with $0<1-f<1$, weakens clustering while leaving the background expansion unchanged.

During matter domination, the growing mode under a reduced clustering strength $1-f$ isIt grows more slowly than the standard $t^{2/3}$ mode whenever $0<f<1$.