on the wavenumber $k$ to be the physical wavenumber expressed in the units of the cosmological horizon, i.e. $k=k_{\text{phys}}/aH$ ($k$ is independent of $H_{0}$ if $k_{\text{phys}}$ is measured in $h/$Mpc). This means that $k$ is time-dependent. We observe galaxies, not matter perturbations, so as anticipated we need to introduce a bias function $b(k,z)$ such that $\delta_{\text{gal}}=b\delta_{\text{m}}$. Without the assumption of a particular model, DE perturbations are unknown. In many models they are not at all small compared to matter perturbations. For this reason, we will define the *total density* perturbation $\delta_{\text{t}}\equiv\Omega_{\text{m}}\delta_{\text{m}}+\Omega_{x}\delta_{x}$ and introduce the bias $B$ of galaxies with respect to it, $$\delta_{\text{gal}}=B\delta_{\text{t}}=BZ\Omega_{\text{m}}\delta_{\text{m}}\,,$$ where $Z(k,a)\equiv1+\Omega_{x}\delta_{x}/(\Omega_{\text{m}}\delta_{\text{m}})$ is a function of space and time that depends on the clustering of the $x$-component. Then we have that $b=BZ\Omega_{\text{m}}$.

Let us denote the initial total density perturbation spectrum at decoupling as $\delta_{\text{t,in}}^{2}(k)$ and as $G_{\text{t}}(k,z)$ the scale-dependent growth function of the linear *total* density perturbations, normalized to unity at present. If the galaxies move with the same velocity field as matter, the galaxy velocity divergence $\theta_{\text{gal}}$ in the sub-Hubble regime is related to the *matter* density perturbation as $\theta_{\text{gal}}=\theta_{\text{m}}=-\delta'_{\text{m}}=-f\delta_{\text{m}}$, by the continuity equation for matter. We then obtain $\theta_{\text{gal}}=-(f/b)\delta_{\text{gal}}$, where $f=G'/G$ is the linear 