Effect of 1b-DDM parameters on the linear (solid) and non-linear (dashed) matter power spectrum. Left: Effect of varying the decay rate Γ_ddm with a fixed fraction $f_{\mathrm{ddm}}^{\mathrm{ini}}=1$. Right: Effect of varying the fraction $f_{\mathrm{ddm}}^{\mathrm{ini}}$ with a fixed decay rate Γ_ddm = (1/13.5) Gyr⁻¹. The other parameters (${\mathrm{\Omega }}_{\mathrm{dm}}^{\mathrm{ini}}$, Ω_b, h, A_s, n_s) are kept fixed, and the spectra are computed today (z = 0). Dashed lines show the predictions of the emulator of Hubert et al. (2021). Our pipeline relies on the prescription of Eq. (16), shown as a dotted line, which smoothly interpolates from the linear to non-linear behaviour.