Matter-spectrum response to extra dark energy ($P_m^{\mathrm{new}}/P_m^{\mathrm{old}}\simeq (D_{\mathrm{new}}/D_{\mathrm{old}}{)}^2$)

With physical matter and radiation densities, primordial amplitudes and spatial flatness fixed, extra smooth late dark energy increases $H_0$ but keeps ${\Omega }_m{H}_0^2$ fixed. Provided the dark energy is negligible at equality, the early cosmological transfer function and equality wavenumber in physical units are unchanged. Earlier accelerated expansion suppresses the linear growth factor, lowering present dimensional matter power by its squared growth ratio. Units involving $h$ can additionally relabel the horizontal and vertical axes.